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Informing Long Term Lumber Buying: A Decision Making Criteria for Wood

Buyers Using a Simple Algorithm

Thanos Gentimis

Louisiana State University AgCenter

Shaun Tanger

Louisiana State University AgCenter

Maria Bampasidou

Louisiana State University AgCenter

Lumber purchasing decisions rely mostly on historic lumber prices, or the corresponding price of their

futures. Various, lumber specific, supply and demand conditions lead to an unpredictable weekly price if

one employs basic economic and statistics tools. We propose a prediction model that builds on the historical

change of the price from week to week to provide purchasing recommendations yearly. We tested our model

using data from the Random Lengths weekly price catalog for six lumber types (1995-2014), comparing it

to other purchasing strategies created from the spot and futures prices showing that it is better almost

always.

INTRODUCTION

Lumber in the United States is a heavily used commodity in manufacturing and housing

construction. Thus, the corresponding lumber markets are well established entities in the world of trade,

and the various lumber prices are the object of speculation from sellers and buyers alike. However, due to

complex supply and demand conditions, these prices regularly exhibit extreme volatility in the short-run

constituting forecasting a difficult task (Oliveira et al., 1977). These conditions can be linked to stumpage

costs, railroad strikes or railcar shortages, residential construction, and prices of substitutes like steel and

aluminum. In addition, the lumber market can be affected by macroeconomic conditions; the housing

bubble of 2006 followed by the great recession in 2009 are recent examples.

Traditionally, forecasting models for purchasing recommendations in lumber depend on historic

price series and futures prices. So far, studies have employed moving average analysis and regression

analysis to forecast lumber price series and address the volatility these series exhibit, by incorporating other

factors, like variables for demand, price movement and volume traded. The complexity of forecasting

lumber price series intensifies when we consider different production and trading regions, different species

and grades, lumber uses and respective dimensions needed. Considering an aggregated lumber price series

for grades, regions, and species implying that the law of one price holds for the lumber market can lead to

misspecifications of the forecasting model (Yin and Baek, 2005). This issue can also be encountered in

studies using futures prices and renders some of these models impractical in extended periods of time.

In this paper, we propose a new prediction model that builds on the movement of prices instead of

their actual values (spot or futures prices). The proposed model complements the existing literature,

utilizing only the aforementioned time series. Specifically, we use data from the Random Lengths weekly

price catalog for six lumber types for the years 1995 to 2014 and no other information. We do not aggregate

our data but instead examine stationarity, correlations between these six series, and seasonality patterns

separately for each price series. Keeping the data series disaggregated allows for a more robust empirical

analysis and targeted purchasing recommendations tied to the respective lumber type.

As indicated, successful buying and selling of lumber is dependent on traders accurately predicting

prices that they will face in the near future (Buongiorno et al, 1984). Many lumber market participants

engage in price discovery through following and/or transacting in the lumber futures market (Deneckere et

al., 1986; Hasan and Hoffman-MacDonald, 2012). Though thinly traded, the trading volume threshold,

which is necessary to facilitate efficient price discovery, is very low, the common price discovery measures

suggest that futures markets are dominant in the price discovery process (Admmer et al., 2016).

Calculations of the referenced authors indicates that only 42 percent of the total production in covered by

the futures market and find that only 1 of the 6 largest lumber trading companies took active positions in

the futures market despite other risk hedging behavior. However, many lumber buyers do not engage this

mechanism of price discovery, relying more heavily on recent prices and experience of trading networks

developed over time. Linkedin correspondence with a lumber trader indicated not all traders use the futures

market to determine buying and selling strategy. While some use it as a basis for contracting, those that

trade in the open markets will look at futures to decide if they should buy or sell. Others simply buy based

on inventory needs and demand that they face in the present. While recent findings in the lumber price

literature suggest that engaging the futures markets is efficiency increasing over not using it, consensus

does not exist on the subject (Parajuli and Zhang, 2016). Given lumber's thinly traded futures, several

researchers have found that spot and futures price series are not co-integrated, implying very little to no

role of futures in the price discovery process for lumber spot prices1.

However, using novel statistical methodology the two most recent publications on the subject, find

that indeed futures do aid traders in the price discovery process (Parajuli and Zhang, 2016; Mehrotra and

Carter, 2017). Two questions arise repeatedly in the literature:

1) Are futures prices merely following the same process as the spot prices due to end use demand? In other

words, are the same expectations and supply and demand conditions that influence spot prices and futures

prices and thus are redundant in the information they provide (Mehrotra and Carter, 2017), therefore

showing co-integration when its spurious? This question, while addressed remains unanswered in the

futures literature.

2) Are lumber futures a strong predictor for specific species that are not included in the futures contract?

For example, can futures be used to predict prices for southern yellow pine? “The species mix in the futures

contracts is a significant component of North American lumber production, but it does not represent the

majority of the softwood lumber produced. We estimate that 20-25 percent of the softwood lumber

produced in 2009 was of species that could qualify for the contracts.”(Lutz, 2012, p.3). Lumber futures are

comprised of 2x4’s (8’ to 20’), graded at #1 and #2 of western SPF, Hem-fir, Engelmann Spruce, and

Lodgepole pine. This question has been examined empirically, but the evidence is mixed. However, if there

are strong correlations among lumber species, seemingly, the answer should be yes.

Yin and Baek (2005), undertake the most ambitious analysis on the subject of co-integration among

lumber species in the North American market. They find evidence supporting the law of one price for the

entire United States softwood lumber market (in other words, co-integrated), but unlike the futures and spot

prices literature there is far more agreement on the matter (Uri and Boyd, 1990; Jung and Doroodian, 1994;

Shahi et al., 2006; Shahi and Kant, 2009). They do mention that this relationship is not unanimous among

price series relationships. However, depending on the test groupings were co-integrated approximately 90

percent of the time, no matter the test.

Unfortunately, the same statistical question plagues this literature on the issue of co-integration as

that mentioned by Mehrotra in the futures prices literature. Namely, that species may be co-integrated, but

not due to substitutability, instead owing to the fact that all these co-integrating relationships are caused by

common-demand side factors (Shook et al., 2009). Softwood lumber is largely traded through wholesalers,

who can take speculative positions on a number of species through storage of the commodity and hold long

positions on a number of lumber species. Thus, prices for various species may show co-integration due to

liquidity constraints faced by the wholesalers, who trade multiple species concurrently (Pindyck and

Rotemberg, 1988; Shook et al., 2009). Regardless of a causal relationship, this would indicate that prices

for various lumber species are highly correlated and thus the futures should adequately predict any lumber

type prices including the southern yellow pine lumber we examine in this paper especially the #2 series.

On the other hand, there are several researchers who have examined the relationship of other

specific spot prices and the futures market and have not found this to be true (e.g. Hasan and Hoffman-

MacDonald, 2012; He and Holt, 2004; French, 1986; Fama and French, 2016). Mehrotra and Carter (2017)

believe this may be either due to the species differences in the lumber futures and spot prices, since the

specific lumber commodity traded on the futures market is not traded in any spot market, or due to a

statistical averaging issue common in time series (using monthly or quarterly averages). They use the price

of the expiring contract to serve as a spot price (thus removing the species mix issue). However, Parajuli

and Zhang (2016) using the same specific species series as Manfredo and Sanders (2008) do find co-

integration between the two series. This would indicate that the lack of integration is due to some other

factor(s). In fact, it may be a specification issue with how the authors are constructing their futures price

series, specifically the expiration date and when the price rolls over to the subsequent futures series. Parajuli

and Zhang (2016) use a continuous weekly series similar to that developed by Quandl. Interestingly, the

implications of these more recent findings, is that futures can be used as a hedging mechanism against

market volatility and as advance information of lumber markets.

While many researchers have devised various models and methods to examine the relationships of

lumber prices, those that employ futures or otherwise, do not reach the same conclusions. It may in fact be

the case that the series are exhibiting long memory (Niquidet and Sun, 2012), which may explain why at

times, two or more price series may co-integrate, but at other times they do not (a common issue in the

futures literature). Niquidet and Sun (2012) examine several lumber and pulp products and find that after

price shocks, despite the shock dissipating within 50 months, the effects can linger for 30 years. Among

lumber markets, Sun and Ning (2014) find that the southern markets tend to achieve equilibrium more

quickly than those of other North American lumber markets after price shocks. Assuming the co-integration

is true, one could use the delayed futures price to predict the movement of the actual price. Unfortunately,

our model neither confirmed, nor denied the existence of co-integration in a definite way, as we will explain

in section results.

In terms of forecasting lumber prices, the papers by Oliveira et al., (1977), Buongiorno et al.,

(1984), and Deneckere et al., (1986) are the most relevant to our analysis. Using a series of models from

ARIMA, Oliveira et al. (1977), found these simple time series models to be relatively accurate for short-

run predictions of lumber prices (within 10 percent of actual prices up to 4 weeks for SYP). Buongiorno et

al. (1984), compared a relatively complex econometric model, a futures model, and a lagged cash price

model in terms of predictive power. In the shorter-run (one quarter), FORSIM and futures models compared

favorably, but for longer term forecasts (2-3 quarters) the FORSIM model was superior. Both outperformed

the lagged cash price model. Further, findings in Deneckere et al. (1986), indicate that futures are an

effective hedge to blunt the variance of cash positions taken by the trader, making them effective for risk

averse traders.

The only other literature we were able to find on the issue of a decision framework for buying and

selling lumber was Kingslien (1975). They give an explicit methodology for producers to sell futures once

agreeing to contract to produce lumber, they also state that wholesalers and end purchasers can use the

tables with a simple formula to determine desired futures selling prices (i.e. Desired profit margin + Cost

of production - Adjustment factor for item(s) = Futures price). Then using their tables to arrive at the

adjustment factor, they offer producers guidelines for trading futures, given relationships that they establish

between non-contract and contract grade lumber prices and how they are related to expiring futures prices.

In this paper, we take a slightly different approach to advance the literature by adding this

interesting applied wrinkle: Given historical information in the respective weekly price series (futures or

spot), what action should be taken by lumber buyers (buy or don’t buy)? Specifically, we offer purchasing

recommendations based off probabilities of price movements rather on actual prices. We compare this

“long-history” model against other possible strategies to determine the best strategy to use over a given

period (2000-2015). Our findings indicate that among model alternatives, our model outperforms all other

strategies, including one that uses futures prices with up to six months of lags. We also examine these

recommendations in the context of warehouse space that the buyer has available. This has implications both

for the literature on futures and spot lumber prices and their relationships as well as real world implications

for buyers who wish to employ this method as a buying strategy for purchasing lumber throughout the entire

year. Our paper is structured as follows. The data section, discusses the lumber price series used in the

analysis and examines some of their properties, namely potential trends, correlations and seasonal patterns.

The following section, introduces the mathematical underpinnings of our model's estimation algorithm,

formulates the conceptual model and describes the computations. In the subsequent section, we compare

our model to others for various parameters and report our results. In the last two sections, we discuss our

findings in terms of main economic conditions and conclude this paper by presenting future venues for this

analysis.

DATA

Dataset Description

Our dataset comprises of weekly lumber prices provided by the independent price recording

company “Random Lengths” for two grades and six types of softwood lumber described in the table below

(See Table 1).

TABLE 1

LUMBER PRICE SERIES

Price

Series

Pubdate

Description

Price

Year

Month

Week

Issue

LAGD

06-Jan-95

KD Southern Pine

(Eastside) #2 2x4

random Prices Net f.o.b.

Mill

420.00

1995

1

1

1

LAGD

13-Jan-95

KD Southern Pine

(Eastside) #2 2x4

random Prices Net f.o.b.

Mill

425.00

1995

1

2

2

LAGD

20-Jan-95

KD Southern Pine

(Eastside) #2 2x4

random Prices Net f.o.b.

Mill

420.00

1995

1

3

3

LAGD

27-Jan-95

KD Southern Pine

(Eastside) #2 2x4

random Prices Net f.o.b.

Mill

408.00

1995

1

4

4

Lumber products come in different grades, which are often related to the quality of the sawlog,

originally harvested and converted to the corresponding wood product. Typically, these are some form of

structural lumber (i.e. 2x4, 2x6) or plywood depending on the size and quality of the original sawlog.

Softwoods (or pine) such as these under examination in this manuscript, come in four grades based on either

their strength and/or appearance. Knots and other defects result in a lower grade. Most two-inch thick

softwood lumber (the 2 in 2x4) is graded for its strength rather than appearance.

The common grades found at your local lumberyard from best to worst are:

#1 Construction grade, #2 Standard grade, #3 Utility grade and #4 Economy grade. This study originated

from a collaborative project with a wood pallet producer in the Southeastern United States. Typically,

pallets used for shipping and hauling products utilize #4 grade quality lumber. However, many chain stores

(e.g. Walmart, Lowes) use #2 grade for floor displays of merchandise. This particular pallet producer

creates pallets for both of these uses, utilizing the lumber dimensions listed earlier in the text and thus our

analysis focuses on these particular lumber products. While we cannot make any generalizable claims about

other lumber species and how well our model performs relative to other predictive models, we see no reason

why this analysis could not be done to estimate purchasing options for other lumber types or other popular

wood products, such as plywood and engineered wood products.

The dataset covers the period of 1995-2014 and it was pre-processed to fit a standard 52-week

calendar with appropriate interpolations. In the original dataset, all months had 5 weeks, but some of them

had no entries. We found the weeks with the fewest entries throughout our dataset for each lumber type,

and removed them until a 52 week calendar was created. This may result to a small error in computations,

but since the comparisons are averaged out over many years, we do not anticipate that to be a major flaw.

A typical entry (row) of our dataset is presented in the table below (See Table 2) and our dataset has 6,240

rows. We use the dataset to perform both the training and testing of the model in this paper, but we plan to

expand our methods to other types in the future.

TABLE 2

TYPICAL ENTRY OF DATASET

Price Series

Description

Year

Week

Price

LAGE

KD Southern Pine (Eastside) #2 2x4 random Prices Net

f.o.b. Mill

1995

1

395

Trends and Graphs

In this subsection, we present some simple descriptive statistics of our dataset and the associated

graphs. We viewed each lumber type as a separate time-series thus creating the graphs in Figure 1.

FIGURE 1

PRICES FOR VARIOUS LUMBER TYPES FOR THE YEARS 1995-2014

To check for stationarity and explore the attributes of our dataset we examined each price series

separately. The first three panels in Figure 1 (top row) are for grade #2 2x4, 2x6 and 2x8, respectively,

whereas the next three panels (bottom row) are for grade #4 2x4, 2x6 and 2x8, respectively. As we see in

Figure 1, there are no clear periodic behaviors overall but a further analysis of each time series separately

revealed some seasonality which we comment on below. Our analysis of the one week lagged price

differences showed that the week by week differences are not (statistically) significantly different than zero

throughout the years. Table 3 gives the relevant statistics.

TABLE 3

STATISTICAL ANALYSIS OF THE ONE WEEK DIFFERENCE IN PRICE PER

LUMBER PRICE

Price Series

Mean

St. Dev.

SE

Tstat

Min

Max

LAGD

0.013

8.509

0.264

200.871

-35

53

LAGE

-0.023

9.228

0.286

139.792

-36

40

LAGF

-0.043

9.588

0.297

134.535

-40

40

LBPO

0.082

3.323

0.103

174.709

-20

18

LBPP

0.038

3.691

0.114

157.272

-20

18

LBPQ

0.059

3.485

0.108

138.808

-25

15

We then tried to identify common peaks and lows for the price of each individual lumber type over

the span of a year. In Figure 2, left panel for example, we plot the weekly prices for type LAGD for the

period 1995-2014. No clear trend can be discerned. This holds for the other five lumber types. Even when

we focus on the last five years of our study period, trends are not easy to see on a yearly basis as shown in

Figure 2 right panel.

FIGURE 2

LAGD WEEKLY PRICES FOR PERIODS (1995-2014) & (2012-2014)

We used the autocorrelation function both on the reported prices and on the one-week price

differences but no immediate periodic behavior was apparent. As one can see in Figure 3 and Figure 4, the

levels rarely exceed the $0.2 mark independent of how many lags we considered.

FIGURE 3

AUTOCORRELATION OF THE WEEKLY DIFFERENCE IN PRICES BY LUMBER TYPE

AND VARIOUS LAGS, PERIOD 1995-2014

FIGURE 4

AUTOCORRELATIONS OF THE PRICES BY LUMBER TYPE AND VARIOUS LAGS,

PERIOD 1995-2014

Our analysis revealed some seasonality in the quarterly price over the last five years as Figure 5

suggests, but again nothing definitive. For example, we see a spike on the price for the second quarter

followed by an average dip on the third quarter. Notice again some variations among years not only in the

pattern the prices for each lumber type exhibit but also at the levels. The normalization to 52 weeks had

minimal effect on the trend since we are averaging over a 13-week period.

FIGURE 5

QUARTERLY PRICES FOR ALL LUMBER TYPES FOR THE YEARS 2010-2014

One can thus suggest that the data, in its entirety, indicate stationarity, and no seasonality is

discernible. As an appendix, we included an analysis of our time series using the Dickey Fuller test and we

discuss our findings there, which conform to analyzing the lags.

Correlations

In this subsection, we shift our attention to the correlations between the prices of different types on

a yearly basis. Our observations hint at distinct trends among lumber types based on their number valuation.

Figure 6 presents our findings, where colored in red are all correlations above 90 percent.

We can see that various strong correlations appear among the six lumber types for most of the

years; for example in 2006 all prices are correlated among themselves. This would give credit to the “law

of one price” described in the literature. However, there are years like 2014 that only a few very strong

correlations can be found, which puts the global power of this law into question. In Figure 6, the last sub-

table shows that if the prices are treated as a long time series (1995-2014) the correlations are stronger

among the types that share a number valuation rather than between grade valuations (#2 vs. #4). This is

something worth exploring in future publications. Notice also that in general many correlation coefficients

are large, close to 0.9. This correlation can be explained if one thinks about the common uses of these types

of lumber as it was described in subsection dataset description above. In Figure 7 we provide more

information regarding the correlations between different lumber prices for all years.

FIGURE 6

CORRELATIONS BETWEEN DIFFERENT LUMBER TYPES FOR THE YEARS 1995-2014

FIGURE 7

CORRELATIONS BETWEEN DIFFERENT LUMBER TYPES FOR ALL YEARS

Once more, we would like to comment that lumber price series are characterized by high volatility

especially in the short-run. In addition, lumber price series are sensitive to market fluctuations including

the lumber market (use of lumber, regions, etc.) and the housing market as well as macroeconomic factors

like interest rates (e.g. Karali, 2011). These factors could help explain the price variation we observe

throughout the years and suggest that no simple model like a regression or moving average would fit the

data series well. Although our model did not exploit the connections we identified, we will surely be

pursuing that venue in future publications.

MODEL

The analysis above indicated that a clear forecast of the weekly price is intractable. In this section,

we present a conceptual model that relates buying strategies to predicted movement of prices. Our models

aims at identifying the turning points, which seemed more stable through the years.

Conceptual Model

We consider an agent, a lumber buyer, who has historic data on lumber prices (spot or futures can be

considered). Each week, the agent makes purchasing decisions based on the direction he or she anticipates

the prices will move based on the forecast and disregards the spot price. This setting allows us to discretize

the price in the following sense. Every week there are three possible scenarios: “The price will go up from

the previous week, the price will go down, or the price will stay the same.”

Let X1, X2,…

,

X52 be random variables corresponding to the purchasing decisions, one for each week.

For each of the Xi

we have three possible directions:

1) ,=The price goes up from the previous week.

2) ,=The price stays the same as the last week.

3) ,=The price goes down from last week.

Due to the cyclic nature of the yearly calendar, week 1 uses week 52 as a previous week with minor

adjustments. FIGURE 8

MATHEMATICAL DESCRIPTION OF THE STATES

We can compute the conditional probabilities ( =,|=,) for all possible cases on

the assumption that the variables and are not independent. The purchasing decision for week i may

affect the purchasing decision for week i+1. To make predictions stronger, we also compute the two-step

conditional probabilities, i.e. ( =,|=,, =,). Clearly, these probabilities change

throughout the year and seasonality is easier to uncover using aggregate historical data in this setting.

We propose three weekly purchasing recommendations for our buyer, namely “Don't Buy (DB),

Buy (B+), and Fill the inventory (B++).” The (DB) and (B++) options are self-explanatory. The (B+)

strategy allows the buyer to satisfy immediate demand and store some extra units for future applications.

In our implementation, the (B+) strategy corresponds to buying twice as much as the needed quantity (2

units) but that can be changed at will. The aggressive purchasing strategy (B++) is not uncommon when

there is lack of information or uncertainty and in our implementation is driven by two consecutive

indications of increased lumber prices for the weeks that follow although again that can be extended to a

bigger time period for other examples. The aggressive buying strategy could be justified with the buyer

making sure they capitalize on a forecasted big increase in prices.

Predictive Model

Our method uses a greater than five year history period (training period) to identify the movements

in lumber prices for the selected period. Additional inputs include, the starting year for the predictions, the

lumber type; the storage capacity and how long of a history should be included in the prediction. In our

implementation, all previous history is included up to the selected year.

Two new variables are created; one that contains the prices forwarded by one week (FOW1) and

another one where prices are forwarded by two weeks (FOW2). The direction is captured by the difference

between the current price and the two forward prices (FOW1 and FOW2) and turned into an indicator

variable with values, +1 if the price goes up, -1 if the price goes down and 0 if it is unchanged. For the last

two weeks (week 51 and week 52) prices from the next year are utilized, and when those are not available,

they are extrapolated using past prices from these weeks.

For each week, the model computes the probability of the price change in the next two weeks using

the selected years as follows:

=(1 > ) , =(1 < ),=(1 = ) (1)

=(2 > ) , =(2 < ),=(2 = ) (2)

Obviously ++= 1 and ++= 1. Finally, the model creates purchasing

recommendations based on the following three cases:

1) > and >, where = 0.2 is a threshold chosen through experimentation. To

compute this parameter, we tested various alphas with increments of 0.05, on the first 10 years of

the dataset and we chose the alpha with the lowest yearly cost for all lumber types on average. In

this case, we anticipate that on average the price will increase dramatically for both the next two

weeks. Thus, the algorithm suggests an aggressive buy (B++).

2) 0 and 0. In this case, we assume that on average the price will go down or

stay the same the next two weeks. The model suggests a halt on purchasing (DB).

3) Everything else, which means that the prices do not follow a clear trend the next two weeks, but at

least one of the two is on average a little bit greater or equal to the current week's price. The model

recommends a moderate buy (B+).

Model Implementation

Our dataset contains information on six types of lumber and respective prices for the years 1995-

2014. In order for the model to stabilize, we require five years of price series data, so our smallest starting

year is 2000. To allow for the implementation of the predictive algorithm and the three recommendations

(B+, B++, and DB) we impose a lower bound on the storage capacity to be four units. That is the minimal

warehouse size since we require one operational unit and a possible purchase up to three more units. Note

that the variable “units” is an arbitrary measure of quantity and it can be adjusted to the operational schema

of any lumber purchasing entity. Also, note that a smaller storage capacity would disregard the three

purchasing choices. For example, at storage capacity of three units the recommendations (B++) and (B+)

will lead to the same purchasing strategy of purchasing two units.

Although theoretically there is no upper bound to the capacity of the warehouse, we decided to stop

it at nine, presenting us with six different cases to test in our experiment. Thus, following the rule of thumb

we have more than 30 comparisons per year (36 in our case) which leads to safe and easily interpretable

statistical results. Furthermore, when we multiply by the number of years (15) we end up with 540 different

possible test cases.

As mentioned earlier, our algorithm provides information for the forward prices (FOW1, and

FOW2), and the direction of the price change with respect to the current price for the two weeks that follow,

(, and , respectively). A snapshot of the information can be found in Table 4.

TABLE 4

INTERMEDIATE TABLE SHOWING THE ALGORITHM AT WORK

Price

Series

Description

Year

Week

Price

FOW1

FOW2

D

FOW1

D

FOW2

LAGE

KD Southern…

1995

1

395

400

380

+1

-1

LAGE

KD Southern…

1995

2

400

380

380

-1

-1

LAGE

KD Southern…

1995

3

380

380

…

0

…

LAGE

KD Southern…

1995

4

380

…

…

…

…

Using the logic statements above the algorithm outputs a list of recommendations for each week of

that year. A representation of the information we have (after cleaning up the dummy columns) is shown in

Table 5. As a reminder, the recommendation Buy (B+) recommends the purchase of units that will satisfy

immediate demand and some additional units, in our experimentation set arbitrarily to two. One could alter

this to match other purchasing schemes if needed.

TABLE 5

WEEKLY PRICES FOR YEAR 2002 FOR LUMBER TYPE LAGE INCLUDING THE

MODEL'S RECOMMENDATIONS

Price Series

Description

Year

Week

Price

Recommendation

LAGE

KD Southern…

2002

1

395

B++

LAGE

KD Southern…

2002

2

400

B+

…

…

…

…

…

…

LAGE

KD Southern…

2002

52

430

DB

EXPERIMENTAL RESULTS

To test the predictive capabilities of our model we created a purchasing strategy for each year and

each lumber type. We do not allow arbitrage to take place; our agent is only allowed to purchase lumber

units and not sell, hence not taking advantage of potential price differences. We impose two restricting

assumptions: we demand one lumber unit to operate and the warehouse size is limited. The first assumption

is important to satisfy immediate demand for the operation; the second assumption is important for the

implementation of the predictive algorithm and is a realistic restriction. Lastly, our model requires having

the same amount of units (s) in store at the start and the end of each year.

The purchasing strategy, based on the suggestion tables of our model proceeds week by week as

follows: Based on our recommendation table we fill the warehouse if the suggestion is (B++). We buy two

units if the suggestion is (B+), in anticipation of a moderate price increase. Finally, if the recommendation

is (DB) we halt purchases unless the warehouse is empty in which case we buy one unit to cover the

operational needs of the week. In addition, as we get closer to the end of the year our purchases are modified

in such a way so that we do not exceed the amount of units (s) set as our end of the year goal in the

warehouse.

Table 6 shows the proposed purchases, stored quantity and the actual cost per week for the lumber

type “KD Southern Pine (Eastside) #2 2x8 random Prices Net f.o.b. Mill (LAGF),” during the year 2010.

The total cost for that year is computed and compared to the other suggestion models described below.

Notice that although our method does not always predict the correct movement of the spot prices, if one

looks at the overall output for the year then on average the prediction is informative and in most cases leads

to a better yearly purchasing strategy.

TABLE 6

A PURCHASING STRATEGY FOR LAGF IN 2010

Number

TAG

Year

Week

Price

Recommendation

Purchases

Stored

Quantity

Cost

2861

LAGF

2010

1

239

B++

9

1

2151

2862

LAGF

2010

2

247

B+

1

9

247

2863

LAGF

2010

3

264

B+

1

9

264

2864

LAGF

2010

4

287

B+

1

9

287

2865

LAGF

2010

5

308

B+

1

9

308

2866

LAGF

2010

6

326

B++

1

9

326

2867

LAGF

2010

7

333

B++

1

9

333

2868

LAGF

2010

8

327

B++

1

9

327

2869

LAGF

2010

9

317

B+

1

9

317

2870

LAGF

2010

10

304

DB

0

9

0

2871

LAGF

2010

11

302

DB

0

8

0

2872

LAGF

2010

12

310

DB

0

7

0

2873

LAGF

2010

13

320

B+

2

6

640

2874

LAGF

2010

14

337

B++

3

7

1011

2875

LAGF

2010

15

357

B++

1

9

357

2861

LAGF

2010

16

371

B+

1

9

371

2862

LAGF

2010

17

375

DB

0

9

0

2863

LAGF

2010

18

369

DB

0

8

0

…

…

…

…

…

…

…

…

…

2904

LAGF

2010

44

229

B+

2

3

458

2905

LAGF

2010

45

232

B+

2

4

464

2906

LAGF

2010

46

233

B+

2

5

466

2907

LAGF

2010

47

233

B+

0

6

0

2908

LAGF

2010

48

228

DB

0

5

0

2909

LAGF

2010

49

224

DB

0

4

0

2910

LAGF

2010

50

223

B+

0

3

0

2911

LAGF

2010

51

224

B+

0

2

0

2912

LAGF

2010

52

227

B++

0

1

0

In the following subsections, we compare our “long-history” method with other strategies and

recommendation methods, using different warehouse sizes.

Naive Method

The simplest purchasing strategy that will satisfy all the assumptions of our experiment is buying

one unit every week. We call this the “naive method”, and we use it as a first benchmark to prove the

predictive power of our method. Figure 9 shows the difference in yearly cost of our long-history method vs

the naïve method, for all years and all lumber types for various warehouse sizes.

FIGURE 9

LONG-HISTORY METHOD VS NAÏVE METHOD

Note: In red, we report the losses of the long history methods vs the naive one, for all years, all lumber types and

various warehouse sizes with initial quantity 1.

Our long-history method outperforms the naive one more than 95 percent of the times assuming

the starting lumber quantity in the warehouse is one. It is interesting that the naive method performs better

than ours mostly in year 2000 and only for large warehouses during the years 2006 and 2009. For year

2000, an explanation could be that the 5-year history is not enough for our prediction algorithm to compute

the correct yearly movements. Another reason could be the mini recession that hit the lumber market during

that period. A thorough analysis for the years of the recession including 2009 is presented in the section

discussion that follows. If we confine ourselves to a warehouse of size 4 (moderate or average size

warehouse) we win constantly independent of the starting and ending quantity.

Random Method

In order to prove the predicting capabilities of our long-history method independent of the purchasing

schema, we created the “random” purchasing method as follows. For each year and each lumber type a new

recommendation table was created using the same labels (B++, B+ and DB) drawn randomly from a

distribution whose probabilities are equal to the probabilities of (B++, B and DB) in the recommendation

tables of our long-history method.

The algorithm again fills the warehouse when the recommendation is (B++), buys two units when the

recommendation is (B+) and halts purchases if there recommendation is (DB). Once more, we make sure

the demand of one unit is covered weekly and the purchases are adjusted so that at the end of the year we

have the same quantity s in our inventory as when we started.

Our strategy is better than the “random” one 80 percent of the times for warehouse sizes of four to

nine units and a starting quantity of one. We note here that we almost always lose in 2009 against the

“random” strategy as Figure 10 suggests. We discuss this in depth in section Recession.

FIGURE 10

LONG-HISTORY METHOD VS RANDOM METHOD

Note: In red, we report the losses of the long history methods vs the random one, for all years, all lumber types and

various warehouse sizes with initial quantity 1.

Short-term Method

We also implemented a classic “short term” prediction strategy as follows. For each week, we computed

the movement based only on the previous week. If the price went up significantly, we recommend (B++)

in anticipation of a price hike. If it went up by a moderate amount, we recommend (B+) in anticipation of

a moderate price increase. Finally, if the prices went down we recommend (DB) as we believe prices will

keep falling. Our purchase suggestions again follow the rules of meeting demand (i.e. have at least one unit

a week) and adjust so that by the end of the year we have the same starting quantity in storage. To distinguish

big increases vs short increases we computed the mean of the positive increases for each lumber type

throughout the years up to the starting year and used that as a cutoff point.

Once again, the “long-history” method is better than the “short-term” method 78 percent of the

times as can be seen in Figure 11. Again, we see a failure of our method to correctly identify the price

movements in 2009 compared to this one.

FIGURE 11

LONG-HISTORY METHOD VS SHORT-TERM METHOD

Note: In red, we report the losses of the long history methods vs the short-term one, for all years, all lumber types

and various warehouse sizes with initial quantity 1.

Futures Method

Finally, we wanted to analyze the predictive capabilities of the futures price series. We also wanted to test

the assumption that is prevalent in the literature, that the futures and spot price are co-integrated. This would

imply that using delayed versions of the futures price time series instead of the reported price would lead

to a better price forecasting. In our first attempt at creating recommendations from the futures prices, we

repeated our method but replaced the price series with various delayed versions of the futures price up to

26 weeks (roughly half a year).

FIGURE 12

LONG-HISTORY METHOD VS FUTURES METHOD

Note: In red, we report the losses of the long history methods vs the futures one, for all years, all lumber types and

various warehouse sizes with initial quantity 1.

We then computed 26 recommendation tables and found the one that yielded the smallest yearly

costs on average for all lumber types. We then compared that to our own method. The following table (See

Table 7) presents the results of the best futures-based recommendation system against ours. It turns out that

the best performance happens when we chose the non-lagged version.

TABLE 7

PERCENTAGE OF WINNINGS OF THE LONG-HISTORY METHOD VS FUTURES METHOD

FOR VARIOUS LAGS

Lag

Percentage

None

67.22%

1 Week

69.63%

2 Weeks

74.26%

3 Weeks

74.81%

4 Weeks

72.81%

5 Weeks

74.81%

6 Weeks

75%

7 Weeks

79.26%

8 Weeks

83.7%

9 Weeks

84.44%

As one can see our long-history strategy is better than the futures recommendation in the majority of cases

(67 percent). Again, in 2008 and 2009 our method is clearly outperformed by the futures one.

DISCUSSION

Our analysis revealed some interesting results for the period of the recent recession of 2006 to 2010.2 We

found that during this time both lumber prices and housing starts had been dropping since 2006. Lumber

traders recognized the phenomena in late 2005 as volumes of lumber futures reached levels not seen since

1985, which not surprisingly coincided with a large drop in housing starts-although lumber prices generally

moved in a positive direction. As housing starts, lumber prices, and futures prices collapsed, the volume of

futures traded continued to rise, with abnormally high volumes until the trough in housing starts and lumber

prices subsided in April of 2009. Again, futures prices seemed to indicate a recovery as their numbers began

to improve for the first time in January of that year.

Table 8 presents the performance of the methods examined for the six different lumber types and

warehouse sizes four through nine (for a total of 36 cases) for the years 2007-2009.

TABLE 8

METHOD COMPARISONS FOR YEARS 2007-2009

Methods

2007

2008

2009

Long-history

27/36

3/36

5/36

Naïve

0/36

0/36

0/36

Random

9/36

1/36

31/36

Futures

0/36

32/36

0/36

Short-term

0/36

0/36

0/36

It is clear that in 2007, traders believed that markets would rally and they did slightly, as such the

“normal” price histories still do a good job of predicting behavior, however the “random” model performs

second best as credit markets begin to short circuit. By the start of 2008, we are in the designated time of

the credit crisis and lumber traders continue to hedge in large volume futures trading. At this point (January

of 2008) housing starts are at their lowest since 1991. While lumber prices rally slightly in the middle of

the year, housing starts continue to slide. This can be attributed to the steepest lumber production decline

on record (Random Lengths). It is clear that traders are now driving the markets in futures trading as the

futures model dominates the other two. The randomness has been driven from the model, largely everyone's

belief is that the market is contracting and will continue to do so.

Our price histories no longer perform as well, as such a cataclysmic event is not included in their

history. Lastly, and probably the most strangely is the 2009 outcomes, where the “random” model performs

more strongly than either the “long-history" model or the “futures” model. Interestingly, this is right when

the housing market starts to make its recovery, although the recovery is muted as another panic hits in late

summer of 2009 as housing starts start to decline in August and continue down until October, before rallying

again. This U-shaped market shown in Figure 13 seems to cause problems for both the “futures” model

as well as the “long-history” model. Here it is probable that all methods based on historic price series fail

since the market is in full disarray and thus the fact that the “random” model’s recommendations give the

best results for this year should not come as a surprise. It is important here to note that the “naïve” approach

loses all the time to some other model. So even during the years of crisis employing some of the other

models will lead to better results than employing no model at all.

FIGURE 13

SPOT LUMBER PRICES FOR THE YEARS 1995-2017

CONCLUSIONS-FUTURE WORK

Our long-history data predicting model, although simple in its nature, manages to capture effectively the

changes in the price of these six lumber types on a yearly basis. Without the use of other external

information, the purchasing strategies produced almost always exceed the “naïve” and “random” approach.

Once again, in a future endeavor associations between the various lumber prices will be analyzed, since

according to common practice, these types of lumber are used in conjunction with each other for various

constructions and applications.

In this version of our algorithm, we are not concerned about the magnitude of the price change but

only for its direction. In a later publication, the magnitude of price changes will be used to get a better

understanding of the phenomenon. Also, during our analysis, we discovered inconsistencies in the creation

and dissemination of the “futures” time-series. Thus in a future effort we will try to identify the roots of

some of the problems we spotted in the creation of a continuous futures times series, and utilize some

general statistics-driven ideas to create a more robust version of it.

Furthermore, reflecting on the failure of our method to predict well during the times of crisis, we

will be exploring the creation of a switching mechanism to other models, utilizing shorter histories or even

randomness, when various market indices cross specific critical thresholds. Exclusion criteria for various

turbulent years will be implemented, since the time series information from those years could affect

negatively the predicting capabilities of our algorithm when the market resumes its natural cycles.

Finally, we note that due to the simple nature of the information needed, the model and its

extensions can be employed to forecast prices series for other forest products and agricultural commodities.

Our codes where written mostly in the statistical language R and some of the time series analysis utilized

the package “forecast” (Hyndman and Khandakar, 2008). The codes can be made available after a

communication with the authors.

ENDNOTES

1. Information can be found at http://www.cmegroup.com/trading/agricultural/lumber-and-pulp/random-

length-lumber_quotes_volume_voi.html. Trading volume was at 1,244 as of this writing.

2. Officially, the subprime mortgage crisis occurred from December of 2007 and lasted until June of

2009. Housing starts peaked in January 2006, at 2.273 million seasonally adjusted starts. The lumber

futures composite reached its low in January of 2009 and housing starts reached their bottom

approximately four months later, which interestingly enough is the time lag of two futures contracts.

Perhaps futures traders saw evidence of the recovery in their business.

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APPENDIX A. Dickey-Fuller Tests

The Dickey-Fuller test assumes as a null hypothesis that the differences between consecutive elements of

the time series do not depend on the previous values, but are just random errors. We say then that a unit

root is present in our autoregressive model. We tested our time series for each lumber type on the whole

history of our dataset and on the last five years using the specific Dickey-Fuller t-distribution

(computations in R). Table A.1 presents the test results for the whole history and Table A.2 for the last

five years.

TABLE A.1

DICKEY-FULLER TEST FOR EACH LUMBER PRICE (1995-2014)

LAGD

LAGE

LAGF

LBPO

LBPP

LBPQ

p-value

0.007

0.011

0.01

0.01

0.01

0.014

TABLE A.2

DICKEY-FULLER TEST FOR EACH LUMBER PRICE (2010-2014)

LAGD

LAGE

LAGF

LBPO

LBPP

LBPQ

p-value

0.341

0.353

0.421

0.133

0.038

0.142

According to table A.1 we should reject the null hypothesis, i.e. that the time-series has a unit root,

for all types if we view it throughout the years. On the other hand, if we focus only on the last five years

we have a completely different picture, namely according to table A.2 we fail to reject the null hypothesis

for all types except LBPP.

Contacting Author:

Thanos Gentimis, PhD

Assistant Professor, Research

Experimental Statistics

Louisiana State University

53 Martin D. Woodin Hall, Baton Rouge, LA 70803

office 225-578-7205

tgentimis@agcenter.lsu.edu