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The impact of daily weather on retail sales: An empirical study in brick-and-mortar stores


Abstract and Figures

In this study, we examine the influence of weather on daily sales in brick-and-mortar retailing using empirical data for 673 stores. We develop a random coefficient model that considers non-linear effects and seasonal differences using different weather parameters. In the ex-post analysis using historic weather data, we quantify the explanatory power of weather information on daily sales, identify store-specific effects and analyze the influence of specific sales themes. We find that the weather has generally a complex effect on daily sales while the magnitude and the direction of the weather effect depend on the store location and the sales theme. The effect on daily sales can be as high as 23.1% based on the store location and as high as 40.7% based on the sales theme. We also find that the impact of extreme bad and good weather occurrences can be misestimated by traditional models that do not consider non-linear effects. In the ex-ante analysis, we analyze if weather forecasts can be used to improve the daily sales forecast. We show that including weather forecast information improves sales forecast accuracy up to seven days ahead. However, the improvement of the forecast accuracy diminishes with a higher forecast horizon.
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The impact of daily weather on retail sales:
an empirical study in brick-and-mortar stores
Florian Badorf
Kühne Logistics University - KLU
Großer Grasbrook 17, 20457 Hamburg, Germany
Kai Hoberg
Kühne Logistics University - KLU
Großer Grasbrook 17, 20457 Hamburg, Germany
In this study, we examine the influence of weather on daily sales in brick-and-mortar retailing
using empirical data for 673 stores. We develop a random coefficient model that considers non-
linear effects and seasonal differences using different weather parameters. In the ex-post
analysis using historic weather data, we quantify the explanatory power of weather information
on daily sales, identify store-specific effects and analyze the influence of specific sales themes.
We find that the weather has generally a complex effect on daily sales while the magnitude and
the direction of the weather effect depend on the store location and the sales theme. The effect
on daily sales can be as high as 23.1% based on the store location and as high as 40.7% based
on the sales theme. We also find that the impact of extreme bad and good weather occurrences
can be misestimated by traditional models that do not consider non-linear effects. In the ex-ante
analysis, we analyze if weather forecasts can be used to improve the daily sales forecast. We
show that including weather forecast information improves sales forecast accuracy up to seven
days ahead. However, the improvement of the forecast accuracy diminishes with a higher
forecast horizon.
Keywords: retailing, weather, brick-and-mortar stores, regression analysis
1 Introduction
While the weather’s impact on business operations has been studied before (Steele 1951;
Bahng and Kincade 2012), most of the research on the influence of the weather focuses on its
impact on strategic decisions, i.e., mid- to long-term decisions (Chen and Yano 2010; Bertrand
et al. 2015). The weather’s impact on operations (Parsons 2001; Steinker et al. 2017) as well as
on retail sales (Arunraj and Ahrens 2016, Appelqvist et al. 2016) has received only limited
Nevertheless, daily weather, which cannot be appropriately anticipated several weeks or
even months in advance (Simmons and Hollingsworth 2002), has an immediate effect on daily
businesses and sales. Weather, such as precipitation (rain and snow) and temperatures,
significantly influence people’s behavior (Cao and Wei 2005; Murray et al. 2010), although it
is unclear how shoppers change their shopping behavior in physical stores because of the
weather. On one hand, shoppers may choose to exploit good weather, and they may choose to
engage in an outside activity instead of visiting retail stores. Accordingly, they will postpone
or forgo purchases. This consumer behavior can have major impacts on retailers:
“Planalytics found that shopper traffic to specialty apparel stores in major cold-weather markets like
Philadelphia, Boston, and Chicago fell 6%, 5%, and 4%, respectively, during that time. The firm estimates that,
so far this holiday season, apparel-only stores have already lost $343 million through December 12. And that tally
doesn't even include the department stores.
"That Warm Weather You Like Is Costing Retailers Hundreds of Millions", Fortune, Dec 16th, 2015
On the other hand, bad weather might cause shoppers to stay at home and purchase through
online channels instead of physical stores (Steinker et al. 2017), or it might cause them to
change their plans and visit retail stores. Overall, the weather has a significant effect on the
economy. According to Lazo et al. (2011) weather accounts for 3.4% of sales variations.
However, such numbers have rarely been determined for individual businesses. In particular, it
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has not been studied which and how factors affect the weather influence, e.g., store location,
product categories, etc.
From a managerial perspective, it is important to understand such weather influences in more
detail for two reasons: First, managers need to account for the actual weather when analyzing
past sales in an ex-post analysis. Retailers must understand the nature and impact of the different
factors that potentially affected their historical sales. If sales have been affected by particularly
good or bad weather, revenues and sales quantities must be corrected accordingly to enable an
un-weather-biased planning for the future (e.g. to improve order quantities or to avoid
unnecessary mark-downs). Second, managers could use weather forecasts in an ex-ante analysis
to anticipate the impact of the weather on future sales and to improve daily decision making. If
the weather is particularly good or bad, managers could change replenishment quantities from
warehouses or change staff schedules in stores to better align these activities with the more
precise sales forecast.
Studies that examine the influence of weather on businesses often examine the apparel
industry (Chen and Yano 2010; Bahng and Kincade 2012; Bertrand et al. 2015, Babongo et al.
2018). The weather particularly influences the perception of the offered fashion goods.
However, weather also generally affects the shopping behavior, i.e., keeping customers away
from or driving customers into a store. Therefore, the weather also affects sales of non-apparel
product categories, which has not been studied exhaustively. We aim to close this research gap
by explicitly studying the sales of a multi-category retailer that offers a broad range of product
categories from apparel to electronics to kitchen accessories and many more. Earning profits in
the retail industry is tougher than in other industries (Gaur et al. 1999), and retailers are under
pressure to avoid costly mistakes, e.g., over- and/or under-stocking. More accurate forecasts of
customer traffic help to improve workforce planning in stores (Mani et al. 2015), price
optimization and revenue management (Ferreira et al. 2016), and the inventory planning of
stock keeping units (SKUs) (Williams et al. 2014).
Many meteorological service providers offer weather forecasts and weather information to
retailers to improve planning, e.g., MeteoGroup, MetraWeather,, and
Planalytics. Although the application of weather information is widely available in practice, the
academic research has not yet thoroughly investigated the impact of weather on retail sales
(Arunraj and Ahrens 2016). In this study, we leverage the data of 673 stores from a German
retailer to examine the impact of weather on retail sales. We first conduct the ex-post analysis
using actual weather data and develop a new empirical model that incorporates non-linearity
and seasonality. We use the model to quantify the explanatory power of weather information
on daily sales, identify store-specific effects and analyze the influence of specific sales themes
across a broad range of different product categories. Next, we leverage our insights to conduct
the ex-ante analysis using weather forecasts. We analyze how the model can be used to improve
the accuracy of sales forecasts.
The next section reviews the related literature. We describe the data in the third section.
Next, we develop our models, analyze the impact of weather on sales, and discuss the
implications of the results. Finally, we conclude with our scientific and managerial
contributions, limitations, and future research opportunities.
2 Literature
This study addresses and extends the stream of research into the weather’s influence on sales,
in particular on retail sales. To better understand this research issue, we provide an overview
about two aspects of the literature. First, we summarize the factors that potentially link weather
with sales in brick-and-mortar stores. Second, we discuss the existing studies that analyze the
influence of weather on sales.
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2.1 Factors linking weather with in-store sales
Steele (1951) conducted a seminal study identifying four potential factors linking weather to
daily sales: (i) comfortableness, (ii) physical prevention, (iii) psychological effects on shopping
habits, and (iv) desirability of certain products during certain weather periods.
Comfortableness describes a condition under which the weather does not physically prevent
customers from going to a store but creates the feeling that the shopping trip is unpleasant. For
example, workers find that bad weather eliminates distractions and allows individuals to focus
on their work instead of leisure activities (Lee et al. 2012). The comfortableness effect of
weather has been widely studied, e.g., on mood (Keller et al. 2005), automobile plant
productivity (Cachon et al. 2012), stock market returns (Hirshleifer and Shumway 2003),
helpfulness (Cunningham 1979), or product valuation (Zwebner et al. 2013).
Physical preventions are weather-induced hindrances, e.g., snow drifts, which prevent a
customer’s trip even though the customer is willing to visit a store. Physical hindrances in retail
settings are associated with negative effects on contemporary sales (Agnew and Thornes 1995).
Psychological effects may lead to a change in shopping habits, e.g., bulk buying to hoard
supplies. For example, lower prices during an extreme weather occurrence might trigger stock-
ups (Gauri et al. 2017). Lower prices during extreme weather occurrences are common in retail
settings (Beutel and Minner 2012). It has been shown that the weather at the time of purchase
heavily affects customers’ decisions for purchases, e.g., advance sales of outdoor events, when
the weather at the time of purchase should be irrelevant (Buchheim and Kolaska 2017).
Finally, weather might influence the desirability of certain products, e.g., umbrellas during
rainy periods or barbecue grills during sunny and warm weather. Such desirability is most often
observed in the fashion industry (Chen and Yano 2010; Bertrand et al. 2015). For example, cold
winters help the sales of warm winter clothes (Bahng and Kincade 2012), and sunscreen is
sought during warm and sunny weather (Parsons 2001).
2.2 Weather impact on retail sales
Some empirical studies about weather effects adopt a general approach by estimating the
weather’s influence on the aggregated economy (Starr-McCluer 2000; Lazo et al. 2011).
However, those studies do not draw managerial implications from their findings. The studies
that provide managerial implications often consider the weather as a factor in strategic planning
or on aggregate levels.
A common theme in studies of the weather effect is the focus on daily aggregated sales. We
provide a summarizing overview of relevant studies that apply empirical methodology in Table
1. The table focuses on studies on which our research is built upon and whose findings we want
to expand. An overview of the weather factors that are used in retail industry studies is provided
by Arunraj and Ahrens (2016, p.737). Most studies find a clear link between the weather and
retail sales. For example, Parsons (2001) finds that temperature and rainfall affect shopping
behavior and Perdikaki et al. (2012) show that weather and sales link via traffic. However, the
results are aggregated for the shopping center location, not for individual stores and/or products
within the shopping center. Murray et al. (2010) investigate the weather effect on a single store’s
daily aggregate tea sales and find that weather, in particular sunshine, triggers psychological
mechanisms that increase consumer spending. Steinker et al. (2017) find that temperature, rain,
and sunshine have a highly significant effect on daily sales for an online retailers. Verstraete et
al. (2019) propose a machine learning approach to handle the impact of both the short-term and
the long-term weather uncertainty on the forecast (for the former it is automatically selecting
the best prediction model).
Another stream of research studies study unexpected deviations from seasonal patterns and
explore deviations in daily temperature. Bertrand et al. (2015) show that seasons have different
exposure to temperature anomalies, and men, women, and kid’s clothing show different results
in response to the same weather risk. They develop a method to assess weather-related risk in
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sales and show how managers can use weather derivatives to hedge against such risk. In a
similar setting, Choi et al. (2011) find that apparel companies can minimize the cost that is
associated with weather risks by studying consumer behavior. Through a demand prediction
model, they calculate a cost minimizing demand level. Babongo et al. (2018) analyze how
apparel demand forecasts for the upcoming season could be made more accurate by taking into
account the weather of the previous sales season using an extensive data set for winter sports
All prior literature is typically limited in terms of weather variables considered, non-linearity
of the weather impact and data used for the analysis. Most research does not consider weather
parameters other than temperature, e.g. sunshine or rain. While there are some studies that apply
machine learning techniques to investigate the impact of weather on businesses, more
traditional statistical approaches do not include non-linearity and seasonality as
comprehensively in their considerations. When machine learning approaches were used, those
studies did not further investigate the results to gain more insights about the impact of non-
linearity and seasonality on the weather effect on retail sales. When other parameters are used,
the traditional statistical models do not include non-linear effects or seasonality. Finally, the
unit of analysis is often either a single store/shopping mall or single product categories, e.g.
textile, across multiple stores. To the best of our knowledge, Belkaid and Martinez-de-Albeniz
(2017) is the only other study that also considers how the weather effect on sales can differ by
location, season, and product categories. They demonstrate that retailers could increase revenue
by up to 2% through weather-contingent pricing. Their study is embedded in the fashion
industry and neglects non-linearity. Furthermore, they do not quantify the differences in weather
effect on sales that occur due to store-specificity. Our study is closely related to Belkaid and
Martinez-de-Albeniz (2017) with respect to the modeling. While they emphasize revenue
optimization through weather-contingent pricing, we aim to quantify the difference between
linear and non-linear weather effects as well as store- and sales theme-specific effects. By
studying aggregated data, most studies do not incorporate relevant nuances in the weather
effect. Our study seeks to fill this gap by providing a way to determine both aggregate and store-
specific weather effects to contribute to the planning of retail sales on different levels.
Table 1 Empirical studies of daily weather effects in retailing
Weather Effect(s)
variable(s) and level
of aggregation
Steele (1951)
1 department store
for 7 weeks before
Easter from 1940-
Daily total store sales
1 mall location for 6
months from 1995
through 1996
Aggregated daily
shopper count
Murray et al.
1 independent retail
store with 6 years
Aggregated total
daily sales of the
Only for
rature, no
Choi et al.
100 apparel stores for
Aggregated daily
sales of t-shirts and
down jumpers per
Bahng and
52 stores in Seoul
and Kyunggi areas
for 2007-2008
Daily aggregated
Bertrand et
al. (2015)
Fashion retail data
from France for
monthly sales in
volume per
distribution channel
and garment type
Arunja and
3 retail stores (2
food, 1 fashion) in
lower Bavaria,
Germany for 2010-
Total number of daily
transactions, daily
sales data for the
fashion store
Belkaid and
98 fashion retail
stores in 4 European
countries in 13 cities
store footfall and
conversion of visits
into product category
sales per store
mall /
Steinker et
al. (2017)
32 months of online
order data for
customers in one
state in Germany
Aggregated daily
online sales
This study
673 retail stores
across Germany for
2013 and 2014
Aggregated daily
sales per store and
sales theme
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3 Data
For our data set we combine two data sources. We use retail data from a major German
retailer and weather data from a public source. Next, we describe the data in more detail.
3.1 Retail data
The first source of data is the daily sales of 673 stores of a German retailer. The stores are
typically small, with an average size of 80 m², and they are located on pedestrian streets and in
shopping malls. The retailer employs a business model with a constantly changing product
portfolio. Each week the retailer starts and promotes one new sales theme of a product category
in all of its stores, i.e., the same sales theme across all stores at the same time. Generally, the
sales themes consist of 80 to 300 new SKUs that fit common product categories, e.g., rain
clothing and accessories. A sales theme is sold for six weeks (36 days, Monday to Saturday for
6 weeks) before it is retired, i.e., the retailer removes all of the associated products (SKUs) from
its stores. Thus, each week, a different combination of six sales themes is sold within each store.
The offered sales themes vary and cover a broad range of products. For example, in one six-
week window, the offerings were: (1) summer clothing, (2) car accessories, (3) microfiber linen
and silver, (4) children’s beach fashion, (5) bathroom and household articles, and (6) watches.
All of the sales themes are distinct from one another to offer a broad range of product categories.
The sales data include information about the daily sales of 673 retail stores in Germany for
2013 and 2014. The information includes both daily revenue in Euros as well as the number of
SKUs sold per store and article. Because we have such disaggregated sales information, we can
examine both the daily aggregated sales per store as well as the sales by sales theme per store
per day. This offers us additional insights about how weather affects different products. In total,
we have 104 different sales themes in our data (one new per week, retired after 6 weeks).
Furthermore, the retailer provides detailed data about each store location. For instance, the
information includes a store’s size (in m2) and address, and whether the store is located inside
a mall. A particularly important aspect of the sales data is that this retailer does not offer any
price discounts on current sales themes in its physical retail stores before products are retired
from the store, i.e., our data do not suffer from price promotion effects. Furthermore, the retailer
applies a constant advertising effort, i.e., the sales are not actively affected by advertisement
effects. While the retailer uses different channels for advertisements, e.g., an e-mail newsletter
and printed catalogs, they are used in a constant and regular manner, e.g., newsletters are sent
out on the same day every week.
3.2 Weather data
The second data source is the weather data for Germany. We gather the data on the weather
from Deutscher Wetterdienst (DWD), which offers daily aggregate information on numerous
weather parameters free of charge on its FTP servers. We collected the weather information for
a period of 30 years (1985 to 2014). Because the weather is not the same throughout the country
but can vary significantly, we collect the weather information for 79 weather stations. We select
the weather station for each 2-digit zip code, which results in the above mentioned 79 stations.
If a station’s weather parameters are missing, we exclude the specific day. Next, we match each
store to its weather station based on the 2-digit zip code. By using the 2-digit zip code, we
account for the fact that the weather is different across regions; however, we assume that, on
average, the weather is the same within each region. We acknowledge that a 2-digit zip code
can be a spacious area, and some might argue that it does not offer enough location-specific
weather information for different stores within such regions. However, Steinker et al. (2017)
show that the weather within Germany is homogenous enough to use as few as six cluster
regions to sufficiently model differences between locations in Germany with regard to the
weather. Therefore, using as many as 79 weather stations to account for location-specific
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weather information will provide sufficiently specific information for each location. The data
available covers numerous parameters such as the minimum, average, and maximum
temperature, precipitation (rain and snow), sunshine duration, barometric and steam pressure,
and average wind speed. Fig. 1 shows the location of the weather stations (o) and that of the
retailer’s stores (x) across Germany.
Fig. 1 Location of weather stations and retails stores in Germany
Our methodology uses actual weather on a given day to measure the weather’s influence on
sales, i.e., we use observations for temperatured,m,y,l, precipitationd,m,y,l, and sunshined,m,y,l for
day d=1 28 (30, 31) (depending on the number of days of the month), month m = 1… 12,
year y = 1985 … 2014, and weather station l = 1…79. To account for climate changes, we use
a linear trend calculation and calculate detrended weather parameters based on 30 years of data,
i.e., we detrend all of the weather parameters in the regression models (Bertrand et al. 2015).
The World Meteorological Organization (WMO) defines 30 years as the timespan to calculate
normal weather that is not affected by climatic change.
The weather perception on a given day is a combination of weather parameters. For example,
temperature, precipitation, and sunshine are most often used by studies in different
combinations. However, thus far there is no objective measure available to determine how
weather is perceived by humans based on the combination of different weather parameters. To
classify the weather perception on a given day, we derive a classification for each of the three
weather parameters based on the classification of a given day relative to other days of the same
season, i.e., the historical distribution. We do this individually for each season and each weather
station. The 10% percentile represents days with abnormally bad weather (low temperature,
low sunshine and high precipitation), whereas the 90% percentile represents days with
abnormally good weather (hot, no precipitation, and a great deal of sunshine). Each weather
parameter is equally weighted with its respective percentile. We measure the difference from
expected weather represented by the 50% percentile (median weather). Therefore, all of the
plots are adjusted and show no effect from weather for days at the 50% percentile. We assume
theoretical days in which all three weather parameters are observed in parallel, e.g., a 60%
percentile day has temperature, precipitation and sunshine of 60%. In this way, we are able to
calculate an aggregated weather effect for moderate weather occurrences as well as for extreme
ones, e.g., the 10% worst/best days.
A real day can also have a temperature that is ranked at 50%, rainfall at 30%, and sunshine
at 70%. To classify the realized occurrence of weather conditions, we draw on the historical
weather distribution to individually classify each parameter of our 2013-2014 sample for each
weather parameter. We then derive the percentile rank from the historical distribution. After
determining each day’s rank for historical temperature, sunshine duration, and precipitation, we
calculate the average percentile rank of the given day.
Fig. 2 shows the histogram of weather classifications based on their historical percentile
rank. A low percentile rank indicates an abnormally bad weather, and a high percentile rank
indicates abnormally good weather, i.e., days with average percentile ranks that are below 10%
represent abnormally bad weather, whereas days with average percentile ranks that are above
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90% represent abnormally good weather. We find that only 1.8% of the observed days fall into
an average percentile rank that is less or equal to 10%, and only 5.4% fall into an average
percentile rank of 90% or above. If we broaden the definitions for extreme weather to 20%, we
find that 7.7% of days fall into a percentile rank of up to 20% and that 14.7% fall into a
percentile rank of 80% and above.
Fig. 2 Histogram of weather classifications
4 Model development
In this section we introduce our empirical models, which extend the insights gained in
previous studies on weather effects. We amend previous models by including non-linear and
seasonally differenced effects. For our models, we use a log-linear formulation, i.e., we use the
log-transformed daily store sales in Euro as our dependent variable. We apply a log-linear
model because AIC and BIC favor such model specification over a log-log specification and it
provides the semi-elasticities of the weather influences for ease of interpretation, i.e., a change
in sales is expressed as a percentage change while a change in weather parameters is expressed
in absolute values (e.g., percent change in sales by hour of sunshine), which is more intuitive
than a log-log formulation that used a percentage change in the weather parameters (e.g.,
percent change in sales by percent change of hour of sunshine). In addition, an alternative log-
% of observations
Abnormally bad
20% 30% 40% 50%
Weather percentile
60% 70% 80% 90%
Abnormally good
log model would require a rescaling of weather variables (e.g., 0 precipitation or sunshine could
not be interpreted right away) to ensure positive values which would affect the ease of the
Our models include three weather parameters to model the weather effect on daily store
sales. We consider the values of average daily temperature in °C, precipitation in mm per m²,
and sunshine duration in hours, as is outlined in the data section. These weather parameters are
identified, developed, and proven by the prior studies of the weather effect on sales (e.g.,
Murray et al. 2010; Steinker et al. 2017). To verify the fit of the variables in our data, we
examine our model specification for multicollinearity and find that the mean variance inflation
factor (VIF) is 2.1 with a maximum VIF of 5.6 when excluding squared terms. VIFs below a
threshold of 10 commonly do not raise significant concerns about multicollinearity (O’Brien
2007). Further, our own examination of various model specifications indicates that temperature,
precipitation, and sunshine are the most relevant parameters with regard to statistical
significance. We also tested model specifications that include only combinations of the three
variables (e.g., only temperature, only precipitation, or sunshine and precipitation without
temperature); however, those models are prone to endogeneity issues because leaving out
temperature, precipitation, and/or sunshine induces an omitted variable bias and biases the
coefficients of the model.
The prior literature on weather effects suggests seasonal differences in the weather effect
(Murray et al. 2010; Choi et al. 2011). For example, more sunshine has a different effect on
sales in the winter than in the summer. Therefore, we run our models with seasonal variables
per weather parameter. Finally, we include the squared terms because we expect the weather
effect on sales to be a non-linear function of the parameters (Murray et al. 2010; Arunraj and
Ahrens 2016). While using a log-linear specification with a log-transformed dependent variable
induces non-linearity in the model, it does not entirely account for possible non-linear shapes
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in the relationship between sales and weather, e.g., (inverse) u-shapes. Therefore, we include
squared terms to capture such relationships. We additionally tested including a cubed term and
do not find that the relationship between weather and sales are significantly different when we
include cubed terms in comparison to squared terms.
We formulate a random coefficient model (Swamy 1970) that is suitable for panel data and
takes into account the distinction between the stores (Poi 2003; Greene 2012). We use Stata 13
to run the model. It accounts for the stochastic variation of the parameter heterogeneity. This
provides qualitatively similar aggregate results to a fixed-effects model but also provides store-
individual weather effects:
ln(Daily Salesi,t) = αi + β1i,s
temperaturei,t + β2i,s
+ β3i,s
precipitationi,t + β4i,s
+ β5i,s
sunshinei,t + β6i,s
+ γi,w
weekdayi,t + ei,t
where i = 1,..., 673 indicates the ith store unit, and t = 1,..., 624 indicates the time period,
i.e., the day. αi is the store-specific intercept, βi,s are the respective coefficients for the
explanatory variables for each season [spring (March, April, May), summer (June, July,
August), fall (September, October, November), and winter (December, January, February)]
with s = 1,..., 4 and store location i. γi,w are the coefficients for the control variables that indicate
the weekday w (Monday, Tuesday,... Saturday; stores are closed on Sundays). The weather
parameters that we use are the daily temperature (C), precipitation (mm per m²), and sunshine
(hours) for each day t and for each store i. We apply store-specific coefficients, βi,s, for the
explanatory variables for each season to account for the fact that the weather affects each store
differently. Not all of the sales influencing factors are observable to the researcher; the effect
of those factors is captured by the error terms ei,t as proposed by Mani et al. (2015). Note that
the omission of unobservable variables might cause endogeneity. Because the independent
variables for weather are not included in the retailer’s planning process and hence not linked to
the other sales affecting variables, we do not encounter correlation between our independent
variables for the weather and the error term. More specifically, this specific retailer does not
react to day-to-day weather in any way. Obviously, the weather is not influenced by daily sales
of the retailer. Hence, simultaneity is not a cause of endogeneity. Finally, measurement errors
are the third source of potential endogeneity. However, we use daily sales data directly from
the retailer and weather data from the DWD, both of which are not subject to systematical
measurement errors. Therefore, we do not encounter immediate endogeneity.
Table 2 shows the aggregated results of the random coefficient model. Because we are only
interested in the weather effect, we present the corresponding coefficients for the weather
parameters and omit control variables. To gather more insight about the value of weather
information on explaining retail sales, we compare five other model specifications: (i) a control
model without the weather as explanatory variables including only the control variables
(“control”), (ii) a model with weather parameters without seasonality or non-linearity of the
weather effect (“weather”), (iii) a model with non-linearity but not seasonality of the weather
effect [“weather (non-linear)”], (iv) a model with seasonality but not non-linearity of the
weather effect [“weather (seasonal)”], (v) and a model with seasonality and non-linearity of the
weather effect [“weather (complete)”].
The coefficients for the random effects model in Table 2 are the arithmetic mean of store-
specific best linear unbiased predictions (BLUPs), which are similar to the best linear unbiased
estimators (BLUEs) from fixed effects models. Convention distinguishes between BLUEs for
fixed effects and BLUPs for random effects (Robinson 1991). We also conduct the analysis
with a fixed-effects model specification, i.e., coefficients without distinction for the store, and
the results show that the arithmetic mean of the BLUPs is similar in size and equal in direction
to the BLUE coefficients that are calculated by the fixed effects model; thereby providing
robustness to the aggregate empirical results with regard to the weather effect on sales. We find
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that temperature, precipitation, and sunshine duration all influence daily retail sales. Most of
the squared terms are significant, and we can conclude that the effects of temperature,
precipitation, and sunshine are non-linear. Furthermore, the seasonal coefficients are
significantly different and support the notion that the weather affects daily retail sales
differently depending on the time of the year.
Next, we compare the explanatory value of weather parameters in empirical models with
regard to the level of detail of the weather information. The model comparison provides
multiple insights about the weather effect on retail sales. First, our control model that includes
controls for the weekday as well as differences between the stores explains 62.7% of the
variance in daily sales (“control”). As we add the weather parameters to our control model, we
see that the explained variance of the model specifications increases (“weather”). The weather
parameters in our model specifications explain approximately 4.1% of the variance in daily
retail sales above what is explained by the model without weather information. This number is
in line with other studies on the impact of weather on sales (Lazo et al. 2011; Arunraj and
Ahrens 2016). As we further amend the non-linearity and seasonality of the weather effect to
our model specification, we find that the AIC (BIC) drop to 373,930 (374,061) for the non-
linear model and to 350,223 (350,419) for the seasonal model specification from 377,669
(377,767) for the model with only temperature, precipitation, and sunshine. The adjusted
increases by 4.8% (non-linearity) and 7.8% (seasonality), respectively. Finally, we find that the
complete model specification with seasonal-different and non-linear weather effect on daily
retail sales has a AIC (BIC) of only 342,883 (343,210) compared to 409,337 (409,403) for the
model without weather information. Similarly, the adjusted R² increases by 9.2% for the
complete weather information compared to the model without weather information. Hence, we
conclude that the model specification controlling for seasonality and non-linearity of the
weather effect explains more variance in daily retail sales compared to models that include only
a part of the weather information; and it also provides the best fit of the different model
specifications with regard to the AIC and BIC. This is also supported by the MAPE of the
different model specifications. In particular, we find that seasonality explains more variance
than non-linearity. This is in line with the different theories on how weather affects sales.
To illustrate its impact on daily sales, we calculate the difference between days with bad
weather versus days with good weather. We calculate the total daily weather effect based on the
coefficients from our regression model. For this purpose, we derive the empirical distribution
of the three weather parameters. We do this individually for each season and each weather
station. Based on temperature, precipitation, and sunshine, we calculate the weather’s impact
on daily sales based on the deviation from the median weather. Fig. 3 shows the effect for each
season based on the historical weather. The 10% percentile represents days with bad weather
(low temperature, low sunshine and high precipitation), whereas the 90% percentile represents
days with good weather (hot, no precipitation, and a great deal of sunshine). Each weather
parameter is equally weighted with its respective percentile. Because we measure the difference
from expected weather as the difference to the median weather of a season, the plot is
normalized at the 50% percentile.
Table 2 Regression results for weather effect on daily retail sales
(i) Control
(ii) Weather
(iii) Weather (non-linear)
(iv) Weather (seasonal)
(v) Weather (complete)
Temperature Spring
(Temperature Spring)2
Temperature Summer
(Temperature Summer)2
Temperature Fall
(Temperature Fall)2
Temperature Winter
(Temperature Winter)2
Precipitation Spring
(Precipitation Spring)2
Precipitation Summer
(Precipitation Summer)2
Precipitation Fall
(Precipitation Fall)2
Precipitation Winter
(Precipitation Winter)2
Sunshine Spring
(Sunshine Spring)2
Sunshine Summer
(Sunshine Summer)2
Sunshine Fall
(Sunshine Fall)2
Sunshine Winter
(Sunshine Winter)2
Observations (#Stores)
396,246 (673)
396,246 (673)
396,246 (673)
396,246 (673)
396,246 (673)
409,337 / 409,403
377,669 / 377,767
373,930 / 374,061
350,223 / 350,419
342,883 / 343,210
Adjusted R2
t statistics in parentheses, * p < 0.05, ** p < 0.01, *** p < 0.001 Note: Coefficients of the Random Coefficient Model are the means of the store-specific coefficients (BLUPs)
Fig. 3 Weather effect on retail sales
Fig. 3 provides a visual understanding of the impact of weather. First, we see that all four
seasons show different sales reactions to abnormally good and abnormally bad weather. During
the spring, we find the highest positive reaction to bad weather (10% percentile) when sales
increase by almost 15%. However, as the weather gets better the positive sales reaction rapidly
decreases and shows a negative sales reaction to good weather (90% percentile). Summer and
fall are the most similar seasons as both show a positive sales reaction of approximately 4%
during bad weather, which decreases to a negative sales reaction of approximately -8% during
good weather. In contrast, sales in the winter follow an inverse u-shaped relationship to the
weather: bad weather decreases sales by almost 20%; however, as the weather becomes better
the sales reaction is almost negligible except for, again, a negative reaction during exceptionally
good weather of approximately -2.5%. The results for the weather effect intuitively make sense.
As weather gets better, sales in the brick-and-mortar retail stores react negatively. This follows
the argument that customers choose different activities during good weather periods and either
postpone or drop planned purchases. Conversely, sales increase with bad weather during spring,
summer, and fall following a similar argument: customers use physical retail stores relatively
more when they do not engage in alternative activities due to bad weather. However, during the
winter, exceptionally bad weather also leads to lower sales, which follows the argument that
bad weather during winter, when the weather is naturally worse than during other seasons,
constitutes a physical obstacle that prevents customers from purchasing in brick-and-mortar
retail stores. Therefore, our results empirically support the different theories on how weather
affects sales. In particular, we see that customers choose different activities over the purchase
and that weather conditions hinder customers from purchases (Steele 1951; Murray et al. 2010;
Stulec 2013).
Neglecting the non-linearity of the weather effect on sales would impose the risk of over-
and underestimating the weather effect when abnormally good or bad weather occurs. To
illustrate this issue, we calculate the weather effect using the coefficients from the model that
includes the seasonal weather effects [“weather (seasonal)”] but not the squared terms and
compare the weather effect size with the weather effect that we calculate from the model
specification including squared terms [“weather (complete)”]. Table 3 shows the results of this
calculation for abnormally bad and abnormally good weather for each season, i.e., the 10% and
90% weather percentiles, respectively.
Table 3 Weather effect on daily sales: difference between linear and non-linear model specifications
(iv) Linear Model
(v) Full Model
Absolute Difference
* p < 0.05, ** p < 0.01, *** p < 0.001
We find that the weather effect sizes are significantly different between both model
specifications. In particular, we see that the linear model specification underestimates the
absolute effect of weather on daily retail sales when the weather is bad. It underestimates a
positive sales effect in spring, summer, and fall, and strongly underestimates the negative effect
of bad weather in the winter. Meanwhile, the linear specification overestimates the effect of
weather when the weather is good in spring. While the full model results in a negative effect of
2.4% of daily sales, the linear model results in a negative effect of up to 16.4%, seriously
overestimating the negative effect that the good weather in spring has on daily retail sales.
Generally, the linear and non-linear specifications differ between 0.8% and 14.0% with regard
to the weather effect size in cases of abnormally bad and good weather. However, the difference
becomes marginal when the weather does not occur in abnormally bad or good ways but
remains within expectations. As cases of abnormal weather are rare, which also explains the
low magnitude of additional explained variance by the squared term extension in the model, a
linear model specification suffices in the majority of cases. However, in Fig. 2 we see that on
at least 7.2% of days, abnormally bad or good weather occurs. Those are the cases in which
retailers should be aware that a linear model specification could significantly misestimate the
weather effect.
Overall, we found that weather explains a share of variance of historical daily retails sales
and should be considered to be a factor when daily retail sales in a brick-and-mortar
environment are modeled. Furthermore, we find that more elaborate specifications, i.e.,
including seasonally different weather effects and non-linear weather effects, further increase
the model fit and the explained variance for daily retail sales.
5 Analysis of the weather impact on retail sales
For our analysis of the weather impact on retail sales, we use a step-wise approach and
consider different levels of weather information. First, we use our model to ex-post investigate
the location-specificity of the weather effect on historical retail sales, i.e., we examine if and
how weather sales reactions differ between stores. Next, we disaggregate daily sales into daily
sales for each sales theme to analyze how the weather differently affects sales themes. Then,
we apply our model for ex-ante predictions using weather forecasts. We first evaluate hold-out
samples and show next, how weather forecasts instead of actual weather information influence
the sales forecast accuracy.
5.1 Ex-post weather effect analysis
5.1.1 Store analysis
The retailer locates its stores throughout the country (cf. Fig. 1), which leads to a variety of
surrounding conditions. The retailer’s store locations possess different characteristics that
suggest that the weather affects them differently. On one hand, mall locations have paths
between stores that are protected from direct weather influences by roofs, have multiple other
stores in close proximity, and provide a large number of nearby parking spaces. On the other
hand, non-mall locations have paths between stores that are not protected from the weather,
have a smaller number of stores in close proximity and have fewer parking spaces that are not
directly attached to the location. All of these traits have a direct influence on customer
attainability, which is influenced by the weather, and we cannot claim that the weather has a
similar effect on each store (Fergus 1999). Reporting the 24 BLUPs for each of the 673 stores
in our data would be excessive: 16,152 coefficients (673 stores, 4 seasons, 3 weather
parameters, linear and squared effect). Therefore, we calculate the weather effect on sales
dependent on the retail store location and show the condensed results in Fig. 4.
We use the percentile classification for the distinction between abnormally bad weather
(10%), median (expected) weather (50% percentile), and abnormally good weather (90%) as
described in the data section. Fig. 4 shows the box plots of the effects for each store for each
season for all of the weather classifications. We observe a range over which the store effects
differ. During abnormally bad weather the maximum difference in weather effects between
stores is 23.0%, i.e., one store experiences a sales increase of up to 23.1%, and another store
shows a sales increase of only 0.1%, which results in a difference of 23.0% during abnormally
bad weather in spring. This difference between maximum store location specific weather effects
differs across the seasons for abnormally bad weather (5.4% in summer, 8.2% in fall, and 13.2%
in winter). In spring, the maximum difference between stores is 9.1% for abnormally good
weather. For the other seasons, the maximum difference in the weather effects between stores
is 7.6% in summer, 7.4% in fall, and 7.1% in winter. Therefore, we find that the general location,
surrounding, and setting of a store location affects the weather effect on retail sales significantly
with respect to size and in some cases also the direction of the effect.
Fig. 4 Store-specific weather effect
5.1.2 Sales theme analysis
We have examined the weather effect on daily aggregated sales at the firm and the store
level. Those daily aggregated sales consist of product sales from six different sales themes.
Thus, the daily aggregated sales consist of sales from categories that might react differently to
the weather. Therefore, we disaggregate the daily sales into the daily sales per sales theme and
run our empirical model on the disaggregated sales to understand the weather effect on sales
themes. Thus, we obtain 104 results: one for each category that is sold during the two years that
we observe. The dependent variable is the logarithm of a store’s daily aggregated sales in Euros
attributable to a single theme. This gives us the possibility of comparing the weather reaction
between sales themes. Extending our existing model to account for the fact that we analyze the
sales theme level, we formulate the model as follows:
ln(Daily Salesi,t,c) = αi,c + β1i,c
temperaturei,t + β2i,c
+ β3i,c
precipitationi,t + β4i,c
+ β5i,c
sunshinei,t + β6i,c
+ γi,w,c
weekdayi,t + δi,d,c day in sales periodi,t
+ ei,t,c
The new superscript c indicates the sales theme, which we seek to analyze. αi,c is the store
intercept, βi,c are the respective coefficients for the explanatory variables per store i, and γi,w,c
are the coefficients for the binary dummy variables that indicate the day of the week w. We
include dummy variables with coefficients δi,d,c for the day of the sales period d to control for
the decreasing daily sales per sales theme during the sales period. We exclude the seasonal
superscript s because sales themes last only 6 weeks during which the seasonality of the weather
parameter would be difficult to estimate with such short time-series, particularly if we consider
the fact that the majority of the total sales occurs within the first two weeks, which is captured
by δi,d,c.
Table 4 Effect of abnormally bad and good weather on sales themes
Abnormally bad weather (10% percentile)
Abnormally good weather (90% percentile)
Weather effect
Sales theme
Sales effect
Sales theme
(starting week/year)
(starting week/year)
(84 other sales themes)
(84 other sales themes)
We again use the historical weather distribution to show the effects of abnormally bad and
abnormally good weather on the various sales themes. Table 4 shows the effects of abnormally
bad (10% percentile) and abnormally good weather (90% percentile). We report the size of the
weather effect for the ten sales themes with the highest positive and highest negative reaction
in sales dependent on the weather. We find that the reaction to good and bad weather varies
widely by sales theme. For bad weather, the difference is as large as 40.7% (from -14.8% to
25.9%), and for good weather it is even higher, with a difference of 39.3% (from -26.8% to
12.5%). Nine sales themes that are found to react heavily to bad weather are also found to react
heavily to good weather. The direction of their sales reaction is reversed between bad and good
weather, i.e., the sales themes that have higher sales during bad weather show lower sales during
good weather and vice versa. For example, during sales theme 36/2013 the retailer sold rain
clothing and accessories such as umbrellas, which sell well during abnormally bad weather
(+21.3%) but in turn sell particularly badly during abnormally good weather (-26.8%).
However, the retailer sold summer clothing (t-shirts, shorts, skirts, etc.) for men and women
during sales theme 23/2014, which shows the opposite but intuitive reaction that abnormally
bad weather decreases sales (-14.8%) and abnormally good weather increases sales (+12.5%).
To maintain the anonymity of the data we cannot elaborate about the other sales themes in our
data. However, the average difference between abnormally bad and good weather across sales
themes is 13.6% and ranges from 48.8% to 0.1%. Hence, we see that the size of the weather
effect is highly dependent on the sales themes and product categories. Weather-related product
categories such as umbrellas and rain clothing obviously experience a high sensitivity to
weather while the weather does not significantly affect other sales themes, e.g., gymnastics and
fitness (sales theme 3/2014).
Even sales themes that are sold during the same time react differently to abnormally good
and bad weather. Fig. 5 shows the plotted effect for good and bad weather for sales themes that
were sold during six consecutive weeks, i.e., at the same time. Notably, the sales themes that
were sold during the same time show reactions to abnormally good and bad weather that move
into opposite directions, i.e., half of the six sales themes show positive weather effects and the
other negative effects. Two sales themes show a large negative effect on sales while four sales
themes do not show a significant sales reaction to abnormally good weather. We also see that
product categories show a more linear weather effect on sales than aggregated sales at the firm
and store levels.
Fig. 5 Weather effect on six simultaneous sales themes
Fig. 6 shows the box plot of the sales theme differentiated weather effects on sales. It is
comparable to Fig. 4 for the store level effects. Overall, we find that the difference between
sales themes is larger than between store locations. For abnormally bad weather, the maximum
difference for the weather effect between sales themes is 40.7% (23.0% for the store-specific
effect) with an interquartile range of 10.2% (4.0% for store-specific). For abnormally good
weather, the difference between weather effects among sales themes is as large as 39.3% (9.1%
for store-specific).
Fig. 6 Sales theme-specific weather effect
5.2 Ex-ante weather effect analysis
In the previous section, we determined that our model offers ex-post explanatory value by
including weather information. In this section, we evaluate the model’s quality as a mean to ex-
ante include weather information in a sales model, i.e., as a forecasting tool. To achieve this,
we use two analytical steps. First, we leverage a set of hold-out samples to determine the
predictive power of our model using actual weather. Second, we include weather forecast data
and compare the model results against the control model without weather and the model with
actual weather information. As we use weather forecast data up to 10 days ahead of the actual
day, we can further determine up to which point it is beneficial to include weather forecast
information. Thus, we can determine beyond which point inclusion of weather forecast
information does not benefit the sales model’s forecast accuracy.
5.2.1 Hold-out sample evaluation
In Section 4.1 we showed how models with actual weather information, in particular more
detailed weather information (i.e., seasonal and non-linear weather effects), provide better fit
for historical sales data and can help to increase the explanatory power for ex-post sales
analyses. To advance this beyond ex-post analyses, we use a set of hold-out samples and re-
estimate the model coefficients without the hold-out sample data and then predict the sales for
the hold-out samples.
To create the hold-out samples for 2014, we leave one week of each of the four seasons out
of the estimation sample, e.g., week 1, week 14, week 27, and week 40 to create our hold-out
sample A (hold-out sample B: week 2, week 15, week 28, and week 41; hold-out sample C:
week 3, week 16, week 29, and week 42; etc.). Thereby, we create a total of 13 hold-out samples
(hold-out sample A to M). We do this to include one week from each season in each hold-out
sample to show that the model works regardless of seasonality. Then, we estimate the model
using weather information from the actual weather data without data from the hold-out sample
weeks and calculate the predictions for the hold-out samples.
Table 5 shows the results of the hold-out sample estimation with regard to the MAPE of
sales in Euro. We find that for 11 of 13 hold-out samples the model with weather information
improves versus the control model without weather information in terms of MAPE. On average,
the model containing the weather information improves the average MAPE over all hold-out
samples by 1.9 percentage points (a 6.7% reduction in MAPE).
Table 5 Mean absolute percentage error of predictions for hold-out samples
Holdout Sample
without weather
with weather
Holdout Sample
without weather
with weather
5.2.2 Weather forecasts evaluation
To evaluate the value of weather information for sales prediction purposes, it is necessary to
include weather forecasts instead of actual weather information because actual weather
information is only available ex-post but not ex-ante as needed for the predictions. Including
weather forecasts induces uncertainty and forecast inaccuracy in the analysis. Exact weather
forecasts are nearly impossible for longer time periods (Lorenz 1963), and model error in
weather forecast models increases by approximately 100% every 2.5 days (Orrell et al. 2001).
Thus, we use a subsample of our data for which such weather forecast information is
available. While historical, actual weather information is widely available, historical weather
forecasts are not available in the same manner. Hence, we only have historic weather forecast
data for two cities in our data, Hamburg and Frankfurt/Main, in which 41 of the 673 stores are
located. The historic forecasts are available for all three weather variables temperature, sunshine
and perception up to ten days ahead.
We re-estimate the model using weather forecasts as replacements for the actual weather
data and calculate the MAPE of the hold-out samples from 4.2.1 for our subsample of stores
from Hamburg and Frankfurt/Main. We do this for all forecast horizons that are available in the
data, i.e., from one day ahead to ten days ahead of the actual sales day. To evaluate the forecast
accuracy of the model and the different weather forecast horizons, we compare the results with
the control model without weather and the model containing actual weather data calculated on
the subsample containing stores from Hamburg and Frankfurt/Main. Table 6 shows the results
for the MAPE for the subsample of stores from Hamburg and Frankfurt/Main.
We find that the model containing weather forecast information provides a lower MAPE
than the control model without weather information but does not provide lower MAPE than the
model containing actual weather information, which is intuitive as the weather forecasts are
generally inaccurate. However, we also find that the model containing weather forecast
information is on average only marginally better in terms of MAPE than the control model
without weather when weather forecasts for more than four days ahead are fed into the model,
and that the model performs worse for weather forecast more than seven days ahead.
Table 6 Mean absolute percentage error of predictions for hold-out samples including weather forecasts
Model including
Weather forecast for
Hold-out sample
In summary, the results show that weather information, actual weather as well as weather
forecasts, does provide benefits for the prediction but the benefit from weather information
diminishes with longer weather forecast horizons and beyond a certain point does not offer
benefit for the sales prediction.
6 Concluding discussion
A number of prior studies have shown how the weather affects sales in various industries
and in different settings. Our study contributes to this stream of research as we propose a new
model that includes non-linearity and seasonal differences. Using this model, we extend the
previous research (e.g., Arunraj & Ahrens, 2016; Bahng & Kincade, 2012; Bertrand,et al., 2015;
Chen & Yano, 2010) and show how weather affects retail sales in a large number of German
brick-and-mortar stores. Our approach can be used for many different retail settings and across
different geographies.
A first key contribution relates to the finding that the effect of temperature, precipitation,
and sunshine duration on sales is non-linear. The previous studies have hinted but not included
the non-linear effect of weather on sales. We find that weather effect on sales can be over- or
underestimated when a linear versus when a non-linear specification is chosen, and the
differences between a linear and a non-linear approach can be as high as 14.0%. We also show
the significant differences in reactions between seasons, e.g., the sales reaction to bad weather
in fall compared to the reaction in spring or summer. The seasonality of the weather effect has
been observed by some studies (Belkaid and Martinez-de-Albeniz 2017; Steinker et al. 2017)
but has not been stressed and quantified as a necessity for model specifications. The non-
linearity and seasonality of weather effects on sales are of particular importance as they affect
future studies’ approaches, examination, and interpretation of weather influence on sales.
In the ex-post analysis, we provide further insights into store-specific effect and the product-
category-specificity of the weather effect. Although it seems intuitive that weather affects stores
in different locations in different ways, we are not aware of any previous studies that have
explicitly studied this matter. Our model allows for a more distinct approach, i.e., it allows for
the aggregation and the disaggregation of the effect size from firm-specific to store-specific
effects. We find that sales in different stores can differ by up to 23.0% on the same day for the
same weather. Similarly, we show that the weather impact can significantly differ between
different sales themes. We find that sales can increase (or decrease) based on the weather and
the sales theme by up to 25.9% (26.8).
Adding weather information to our control model increases the explained variance between
4.1% and 9.2%, depending on the level of detail of the weather information that is added.
Therefore, we run an ex-ante analysis to analyze how future weather information (i.e. inaccurate
weather forecasts) can be used to forecast future sales. Here, our results are interesting but
somehow mixed. We find that the hold-out sample benefits from weather information.
However, the forecast improvement is relatively low and diminishes with increasing forecast
horizons. For one or two days ahead forecasts, the forecast accuracy improves by up to 1.5%
on average which relates to a relative improvement of 5.7%. For higher forecast horizons, the
benefit decreases, and for seven days ahead, the model falls behind the base model without
weather information.
Our results have important managerial implications. For many applications it is essential for
managers to obtain full visibility on actual sales and to understand the driving factors behind
these sales. We find that the sales can be extremely inflated or deflated based on the weather,
and managers could make wrong decisions by just relying on gut feeling and simple
explanations such as “our sales were good/bad because of the weather”. Using our
methodology, managers would be able to normalize sales data for the weather effect considering
the weather on a given day, the store location and the sales theme. Thus, they obtain a better
understanding on how the products would have sold without particularly good or bad weather.
This could particularly improve decisions on orders for products in the future. From a long-
term perspective, managers can leverage these insights and plan product categories accordingly,
i.e., plan sales themes that balance each other’s reaction to weather. For example, by planning
one sales theme that reacts positively to bad weather and one sales theme that reacts negatively
to bad weather, a retailer is able to offset negative weather reactions and significantly lower its
risk exposure.
Also the results from the ex-ante analysis have managerial implications. In our setting, we
find that the improvement decreases as the weather forecast horizon and error increases, i.e., up
to four days ahead weather forecasts increase the sales forecast accuracy significantly, but
including weather forecasts for more than seven days ahead does not improve the sales forecast
accuracy. Thus, we show managers that including weather information in their planning is only
applicable and beneficial for short forecast horizons and does not benefit their operational
planning more than one week in advance. Accordingly, managers should carefully review the
operations decisions that can be based on the next few days.
Although our study presents a number of novel approaches to the examination of the weather
effects on sales, some limitations constrain our findings. Some of those limitations also provide
new avenues for future research. One aspect of including weather effects in the operational
planning process is the availability of weather forecasts. We use publicly available historic
weather information from the DWD to quantify the effects. Hence, our results represent
Germany; other areas of the world could possibly show different weather effects. Another
limitation of our study relates to the availability of other data. In particular, accurate, historical
inventory data is not available to us. Hence, we use censored demand data based on realized
sales; we are unable to identify lost demand caused by stock-outs. However, exemplary
inventory analyses, for a sample of SKUs, showed that stock-out situations are rare, i.e., lost
sales should play no or a minor role in our sales data. We also do not possess comprehensive
information about customer traffic. Consideration of customer traffic and conversion rates
could open up additional analytical topics, e.g., around staff planning and consumer behavior.
In particular, based on our study we cannot make more sophisticated claims about consumer
behavior in relation with weather effects since we do not have access to the required data. This
would pose a valuable question for future research. Experimental research designs as well as
survey-based studies could provide more insight about how weather affects consumer behavior
and sales for different product categories. Another interesting research path would be to further
examine how weather projections affect consumer behavior and sales since anticipation of the
weather could affect the consumers’ time and shopping planning. Finally, our sales data does
not allow for a more sophisticated control model (e.g., Weber et al. 2017), future studies could
advance our findings by including other sales variables, e.g., product price changes, and their
relation to the weather effect.
Our study provides promising starting points for future research. We want to highlight three
promising approaches. First, we show that analysis of the weather effect does yield a significant
effect that should be considered at various planning stages in retail stores such as workforce
and category planning. However, it is beyond the scope of our study to examine the
consequences of weather effects, e.g., on the inventory planning in retail stores. Future research
should pick up at this point and use different demand patterns to test in which demand scenarios
and at which level of aggregation the consideration and application of the weather effect is
called for. Other retailers might observe stronger effects, and certain product categories will be
affected to a larger degree. For example, perishable goods in supermarkets can be promising
domains for further application of this research because they provide fast-moving, uninterrupted
daily sales. Second, sales shift due to the weather are another potentially worthwhile research
venue. In particular, we are not aware of any study so far that conclusively investigates how
today’s weather affects tomorrow’s retail sales, the day after tomorrow, and multiple days in
advance. Buchheim and Kolaska (2016) conduct such a study on today’s weather on future
outdoor movie ticket sales and Belkaid and Martinez-de-Albeniz (2017) use memory effects as
a robustness check. While we examine the contemporary effect of weather on retail sales, it will
be insightful to gather more understanding if retail sales are lost, postponed, or maybe even
occur earlier when forecasts are known. Third, with the rising importance of machine learning
techniques in research it will also offer a valuable way to further approach the topic of weather
effects on retail sales and business impacts in general. While our statistical approach limits the
potential non-linear effect to a linear combination, machine learning techniques will allow for
a more nuanced view on the impact of non-linearity and seasonality. However, for such
approaches a larger sales data foundation is necessary as training data for the model
specifications that will allow sensitivity analysis in greater detail about the variables' effect on
sales. In this regard we consider our research a starting point for future research by providing
proof of the non-linearity and seasonality that calls for more research in the future.
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... In the interest of space, we will not discuss these papers here. Many recent studies, such as [2,3,5,[28][29][30][31][32][33][34][35][36][37], have controlled for climate in their analyses. For example, ref. [38] was one of the first studies to consider the impact of weather on sales, focusing on the seven weeks prior to Easter over a nine-year period. ...
... While this approach accounts for climate by nature of the panel data, our study takes a simpler approach by using ordinary least squares regression to account for climate and demonstrates the impact of weather on sales. Moreover, ref. [32] constructed a panel model and considered both linear and non-linear relationships but their analysis focused on non-consumable goods. As suggested by the NRF [1], the sensitivity of sales to weather varies greatly depending on the product type. ...
... As suggested by the NRF [1], the sensitivity of sales to weather varies greatly depending on the product type. Furthermore, the complexity of constructing panel data as performed by [31,32] makes it impractical for many real-world settings. Our study highlights the viability of using ordinary least squares regression to account for climate and analyze the impact of weather on sales across different product categories. ...
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In this paper, we explore the importance of accounting for climate when determining the impact of weather on product sales. Using a France-wide scanner panel dataset provided by our industry partner, we show that if climate is not accounted for, product categories may be misclassified as being weather sensitive when they are not, and vice versa. This is motivated by previous research and industry reports that suggest a relationship between weather and retail sales. However, these studies often fail to distinguish between weather and climate, leading to inaccurate conclusions. Our results highlight the need to control for climate in order to accurately assess the effects of weather on retail sales. We use ordinary least squares regression to estimate the relationship between temperature and sales for 29 different product categories. The regression models control for various factors, including shelf space allocation, week of observation, quantity purchased, promotion, store brand, store surface area, store competition, and consumer behavior measures. We find that when accounting for climate, only a subset of the product categories is sensitive to weather. Additionally, we show that climate can be approximated using a week index, eliminating the need for additional data collection and approximation efforts. Our findings have implications for both researchers and practitioners. Researchers should be aware of the importance of accounting for climate when studying the impact of weather on retail sales, as failing to do so may lead to erroneous conclusions. Practitioners can use our results to inform their marketing and sales strategies, taking into account the weather sensitivity of different product categories and the role of climate in shaping consumer behavior. Overall, our study emphasizes the need to consider climate when determining the impact of weather on retail sales, and provides practical insights for retailers and economists.
... While the digital age has posed significant challenges, it has also opened up exciting possibilities for brick-andmortar retail to redefine its role in the modern marketplace. In this article, we will explore the multifaceted strategies and innovations that traditional retailers are employing to secure their future amidst the digital disruption [3]. ...
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The future of brick-and-mortar retail is undergoing a remarkable transformation in response to the digital age. This article explores the evolving landscape of traditional retail, highlighting key strategies that are shaping its future. Enhancing the customer experience is at the forefront of retail evolution, with technologies like augmented reality and data analytics creating immersive and personalized shopping journeys. Click-and-Collect and BOPIS models bridge the gap between online and offline shopping, offering convenience and immediacy while increasing foot traffic to physical stores. Sustainability practices have become paramount, driving retailers to adopt eco-friendly sourcing, energy-efficient systems, and waste reduction initiatives. Local and community engagement strategies are redefining the role of physical stores, fostering lasting connections with customers. In this dynamic retail environment, brick-and-mortar stores are not fading but evolving into hubs of innovation and customer-centricity. Adaptation, innovation, and a commitment to the in-person shopping experience are reshaping the future of retail. Introduction:
... [116] Retail and Sales Adjusts inventory based on weather forecasts. [117] Tourism and Entertainment ...
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Weather and climate prediction have been crucial in human history for enabling effective agricultural planning, safeguarding against natural disasters, and facilitating strategic decision-making in various sectors. In this context, the need for accurate and timely forecasting is highly significant. Machine learning has the potential to improve the accuracy and speed of weather and climate prediction. This comprehensive survey assesses the efficacy of Machine Learning (ML) and Machine Learning-Enhanced (ML-Enhanced) methodologies in short-term weather forecasting and medium-to-long-term climate prediction. Acknowledging the historical importance of weather and climate prediction as crucial tools affecting human life and societal functions, the paper scrutinizes over 20 methods, highlighting six that appear to be at the forefront of ML applications in meteorological forecasting. While ML shows promising results in short-term weather prediction, its role remains supplementary in medium-to-long-term climate forecasting due to the complexity of climate conditions and limited data samples. The study finds ML to be fast, scalable, and relatively accurate; however, traditional methods remain indispensable, particularly for medium-to-long-term forecasts, where understanding the mechanisms of meteorological changes is pivotal.
... The literature on climateaware forecasting has highlighted many impactful real-world applications: from creating option plans for pre-season planning [3], [4], energy and utility industries [5], [6], to the manufacturing industry [7]. Today, most retailers recognize the impact of weather in their demand forecast [8], [9] and use short-term weather forecasts (e.g., a week ahead) while predicting demand or employ de-weatherization techniques to understand weather-driven demand patterns [10]. In order to effectively perform demand management or inventory planning, decision-makers require accurate and reliable forecasting w.r.t. ...
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Current time-series forecasting problems use short-term weather attributes as exogenous inputs. However, in specific time-series forecasting solutions (e.g., demand prediction in the supply chain), seasonal climate predictions are crucial to improve its resilience. Representing mid to long-term seasonal climate forecasts is challenging as seasonal climate predictions are uncertain, and encoding spatio-temporal relationship of climate forecasts with demand is complex. We propose a novel modeling framework that efficiently encodes seasonal climate predictions to provide robust and reliable time-series forecasting for supply chain functions. The encoding framework enables effective learning of latent representations -- be it uncertain seasonal climate prediction or other time-series data (e.g., buyer patterns) -- via a modular neural network architecture. Our extensive experiments indicate that learning such representations to model seasonal climate forecast results in an error reduction of approximately 13\% to 17\% across multiple real-world data sets compared to existing demand forecasting methods.
... They evaluated three specific challenges posed by emerging technologies in the retail domain: born-digital brands, AI-enabled demand forecasting and product design, and collaborative consumption [18]. Badorf et al. discovered that the weather can have an impact on daily sales in the retail industry and that weather forecast information has a positive effect on the prediction of retail sales [19]. Tomáš Formánek established a correlation between store location and its distance from the city center, the presence of competitor stores, and population density, employing these variables as controlling factors to evaluate the sales dynamics within the retail industry [20]. ...
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Using a people-centered approach to new urbanization, China has committed to building high-quality living environments through improving urban livability and promoting a stronger sense of belonging among residents. Retail stores serve as one of the most immediate and accessible destinations for residents’ consumption, and their spatial configuration has a direct impact on residents’ satisfaction and happiness in their daily lives. In this context, for the present study we selected the central urban area of Lanzhou City as the case study area. Based on POI data and using the daily life circle as the basic unit, we applied methods such as kernel density analysis, hotspot analysis, and the Shannon–Weaver index to analyze spatial distribution patterns of the retail industry. Furthermore, we applied Geodetector to analyze the impacts of four factors that are closely related to the retail industry: economic level, convenience level, market demand, and location. The conclusions are as follows: In the central urban area of Lanzhou, the retail industry exhibits a belt distribution pattern along the Yellow River. The density of distribution gradually decreases from the city center toward the outskirts, forming four prominent agglomeration centers. Overall, within the central urban area of Lanzhou, the spatial distribution of the retail industry at the scale of daily living circles shows that only a small proportion of the industry demonstrates noticeable clustering effects. In terms of spatial patterns, the retail industry at the scale of the daily living circles demonstrates similar characteristics in terms of diversity and agglomeration distribution. It exhibits a decreasing trend from the urban core toward the peripheral areas. The agglomeration distribution pattern of the retail industry in the central urban area of Lanzhou is considerably influenced by market demand, economic level, convenience, and location. The spatial distribution of the retail industry in the central urban area is primarily influenced by economic factors and convenience, while market demand plays a major role and location has a relatively minimal impact.
Purpose – Climate change-induced weather changes are severe and frequent, making it difficult to predict apparel sales. The primary goal of this study was to assess consumers’ responses to winter apparel searches when external stimuli, such as weather, calendars and promotions arise and to develop a decision-making tool that allows apparel retailers to establish sales strategies according to external stimuli. Design/methodology/approach – The theoretical framework of this study was the effect of external stimuli, such as calendar, promotion and weather, on seasonal apparel search in a consumer’s decision-making process. Using weather observation data and Google Trends over the past 12 years, from 2008 to 2020, consumers’ responses to external stimuli were analyzed using a classification and regression tree to gain consumer insights into the decision process. The relative importance of the factors in the model was determined, a tree model was developed and the model was tested. Findings – Winter apparel searches increased when the average, maximum and minimum temperatures, windchill, and the previous day’s windchill decreased. The month of the year varies depending on weather factors, and promotional sales events do not increase search activities for seasonal apparel. However, sales events during the higher-than-normal temperature season triggered search activity for seasonal apparel. Originality/value – Consumer responses to external stimuli were analyzed through classification and regression trees to discover consumer insights into the decision-making process to improve stock management because climate change-induced weather changes are unpredictable.
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With the rapid development of artificial intelligence, machine learning is gradually becoming popular in predictions in all walks of life. In meteorology, It is gradually competing with traditional climate predictions dominated by physical models. This survey aims to consolidate the current understanding of Machine Learning (ML) applications in weather and climate prediction—a field of growing importance across multiple sectors including agriculture and disaster management. Building upon an exhaustive review of more than 20 methods highlighted in existing literature, this survey pinpointed eight techniques that show particular promise for improving the accuracy of both short-term weather and medium-to-long-term climate forecasts. According to the survey, while ML demonstrates significant capabilities in short-term weather prediction, its application in medium-to-long-term climate forecasting remains limited, constrained by factors such as intricate climate variables and data limitations. Current literature tends to focus narrowly on either short-term weather or medium-to-long-term climate forecasting, often neglecting the relationship between the two, as well as general neglect of modelling structure and recent advances. By providing an integrated analysis of models spanning different time scales, this survey aims to bridge these gaps, thereby serving as a meaningful guide for future interdisciplinary research in this rapidly evolving field.
Full-text available
With the rapid development of artificial intelligence, machine learning is gradually becoming popular for predictions in all walks of life. In meteorology, it is gradually competing with traditional climate predictions dominated by physical models. This survey aims to consolidate the current understanding of Machine Learning (ML) applications in weather and climate prediction—a field of growing importance across multiple sectors, including agriculture and disaster management. Building upon an exhaustive review of more than 20 methods highlighted in existing literature, this survey pinpointed eight techniques that show particular promise for improving the accuracy of both short-term weather and medium-to-long-term climate forecasts. According to the survey, while ML demonstrates significant capabilities in short-term weather prediction, its application in medium-to-long-term climate forecasting remains limited, constrained by factors such as intricate climate variables and data limitations. Current literature tends to focus narrowly on either short-term weather or medium-to-long-term climate forecasting, often neglecting the relationship between the two, as well as general neglect of modeling structure and recent advances. By providing an integrated analysis of models spanning different time scales, this survey aims to bridge these gaps, thereby serving as a meaningful guide for future interdisciplinary research in this rapidly evolving field.
The weather has been identified as an important driver of demand and constitutes a major risk for retailers, especially in goods for which usage is affected by weather conditions, such as soft drinks or fashion apparel. Specifically, weather variations change the propensity to visit the point of sales, because travel cost is affected by weather conditions; and they impact differently different product categories, because the reference utility in the mind of the consumer is affected by current weather. We empirically study these two impact dimensions at a large fashion apparel retailer. We find that rain has a large effect on footfall, increasing it in shopping mall stores and decreasing it in street stores, which suggest that it is a first-order factor for channel choice. Temperature has a milder effect on footfall. In contrast, temperature has a large impact on conversion, increasing sales of the “appropriate” categories: summer items are sold more under positive temperature shocks, and winter items less. Finally, although theory suggests that the weather should have a moderating effect on price sensitivity, we find that it is unaffected by the weather.
Monthly fluctuations in consumer spending are often attributed to the weather. This paper presents a model in which weather affects the productivity of time in nonmarket activities (such as shopping or recreation), and so, via time and budget constraints, may induce substitution in spending across goods and over time. Using monthly data on retail sales and weather data from the National Weather Service, I find that unusual weather has a modest but significant role in explaining monthly sales fluctuations. However, lagged effects often offset original effects, so that weather's influence tends to wash out at a quarterly frequency.
Accurate demand forecasting is of critical importance to retail companies operating in high-volume low-margin industries. Inaccuracies in the forecasts lead either to stock-outs or to excess inventories, resulting in either lost sales or higher working capital, and for both cases in extra unnecessary costs. Prediction accuracy is essential to retail companies having a part of their product portfolio manufactured in low-cost countries and requiring long delivery times. It is rather vital when the demand for these goods is strongly weather dependent. The combination of long delivery times and weather dependence creates a business challenge, as the availability period of accurate weather information is much shorter than the lead time. In this paper we propose a methodology that handles the impact of both the short-term (with available weather data) and the long-term weather uncertainty on the forecast. For the former, the proposed framework is capable of automatically selecting the best prediction model. For latter, the framework fits a distribution on simulated and aggregated sales using the short-term regression model with historical weather data. This framework has been tested on a company's sales data and is proven to satisfactorily address the challenges that the company is facing.
In seasonal business, manufacturers need to make major supply decisions up to a year before delivering products to retailers. Traditionally, they make those decisions based on sales forecasts that in turn are based on previous season’s sales. In our research, we study whether demand forecasts for the upcoming season could be made more accurate by taking into account the weather of the previous sales season. We use a ten-year dataset of winter sports equipment (e.g. skis, boots, and snowboards) sales in Switzerland and Finland, linked with daily meteorological data, for developing and training a generalised additive model (GAM) to predict demand for the next season. Results show a forecasting error reduction of up to 45% when including meteorological data from the past season. In our case, the value of this reduction in the forecasting error corresponds to around 2% of total sales. The results contribute to the theory of stochastic inventory control by showing that taking into account external disturbances, in this case the fluctuations in weather, improves forecasting accuracy in situations where the lag between ordering and demand is around one year.
The received wisdom, reflected in popular marketing textbooks, is that featuring deeply discounted items will generate additional store traffic for retailers that in turn will lead to increased sales and profits. However, there is surprisingly little systematic evidence about the impact of these deep discounts on aggregate store traffic, sales, and profits. In this paper, we study the effects of promotional discounts and their characteristics on various store performance metrics employing a store level dataset pooled over 55 weeks and 24 stores. Many findings of our study lend credence to the continued popularity of such promotions by retailers. We find that feature promotions build store traffic, especially when the categories being featured are high penetration, high frequency. Also, promotions of branded items are found to be more effective than promotions of unbranded items. Discounting on more items in a category leads to lower store margins suggesting that the cost of discounting a large proportion of items in a category may not be justified by the profits generated by the sale. Using the coefficients from our model estimates, various counterfactuals provide insights into strategic change in level of discounts across categories. We discuss several implications of our findings for retailers.
To be efficient, logistics operations in e-commerce require warehousing and transportation resources to be aligned with sales. Customer orders must be fulfilled with short lead times to ensure high customer satisfaction, and the costly under-utilization of workers must be avoided. To approach this ideal, forecasting order quantities with high accuracy is essential. Many drivers of online sales, including seasonality, special promotions and public holidays, are well known, and they have been frequently incorporated into forecasting approaches. However, the impact of weather on e-commerce operations has not been rigorously analyzed. In this paper, we integrate weather data into the sales forecasting of the largest European online fashion retailer. We find that sunshine, temperature, and rain have a significant impact on daily sales, particularly in the summer, on weekends, and on days with extreme weather. Using weather forecasts, we have significantly improved sales forecast accuracy. We find that including weather data in the sales forecast model can lead to fewer sales forecast errors, reducing them by, on average, 8.6% to 12.2% and up to 50.6% on summer weekends. In turn, the improvement in sales forecast accuracy has a measurable impact on logistics and warehousing operations. We quantify the value of incorporating weather forecasts in the planning process for the order fulfillment center workforce and show how their incorporation can be leveraged to reduce costs and increase performance. With a perfect information planning scenario, excess costs can be reduced by 11.6% compared with the cost reduction attainable with a baseline model that ignores weather information in workforce planning. This article is protected by copyright. All rights reserved.
The consequences of many economic decisions materialize only in the future. To make informed choices in such decision problems, consumers need to anticipate the likelihood of future states of the world, the state dependence of their preferences, and the choice alternatives that may become relevant. This complex task may expose consumers to psychological biases like extrapolative expectations, projection bias, or salience. We test whether customers are affected by such biases when they buy advance tickets for an outdoor movie theater, a real-world situation that, because of the availability of reliable weather forecasts, closely resembles a stylized decision problem under risk. We find that customers’ decisions are heavily influenced by the weather at the time of purchase, even though the latter is irrelevant for the experience of visiting the theater in the future. The empirical evidence cannot be fully explained by a range of candidate rational explanations, but is consistent with the presence of the aforementioned psychological mechanisms. This paper was accepted by John List, behavioral economics.