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Forecasting tourism demand using
consumer expectations
Oscar Claveria and Jordi Datzira
Abstract
Purpose – There is a lack of studies on tourism demand forecasting that use non-linear models. The aim
of this paper is to introduce consumer expectations in time-series models in order to analyse their
usefulness to forecast tourism demand.
Design/methodology/approach – The paper focuses on forecasting tourism demand in Catalonia for
the four main visitor markets (France, the UK, Germany and Italy) combining qualitative information with
quantitative models: autoregressive (AR), autoregressive integrated moving average (ARIMA),
self-exciting threshold autoregressions (SETAR) and Markov switching regime (MKTAR) models. The
forecasting performance of the different models is evaluated for different time horizons (one, two, three,
six and 12 months).
Findings – Although some differences are found between the results obtained for the different
countries, when comparing the forecasting accuracy of the different techniques, ARIMA and Markov
switching regime models outperform the rest of the models. In all cases, forecasts of arrivals show lower
root mean square errors (RMSE) than forecasts of overnight stays. It is found that models with consumer
expectations do not outperform benchmark models. These results are extensive to all time horizons
analysed.
Research limitations/implications – This study encourages the use of qualitative information and
more advanced econometric techniques in order to improve tourism demand forecasting.
Originality/value – This is the first study on tourism demand focusing specifically on Catalonia. To date,
there have been no studies on tourism demand forecasting that use non-linear models such as
self-exciting threshold autoregressions (SETAR) and Markov switching regime (MKTAR) models. This
paper fills this gap and analyses forecasting performance at a regional level.
Keywords Tourism, Forecasting, Consumers, Spain, Demand management
Paper type Research paper
1. Introduction
Catalonia is one of the 17 autonomous communities in Spain. It is located in the north-east
and its capital is Barcelona. Its population (over seven million inhabitants) represents 16 per
cent of the total population of Spain. Catalonia is a tourist region: over 14 million foreign
visitors come to Catalonia every year, leading to 111 million overnight stays and tourism
accounts for 12 per cent of GDP and provides employment for around 19 per cent of the
working population in the service sector. The study of aggregate tourism demand helps the
making of business decisions and tourist policies and provides in-depth information about
tourist flows. Although studies have been undertaken for other countries, to date, there has
not been any analyses of tourism demand forecasting in Catalonia.
Consumer surveys have become an essential tool for gathering infor mation about different
economic variables (Ludvigson, 2004; Garrett et al., 2004; Howrey, 2001). Their results are
weighted percentages of respondents expecting an economic variable to increase,
decrease or remain constant. Therefore, the information refers to the direction of change but
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VOL. 65 NO. 1 2010, pp. 18-36, Q Emerald Group Publishing Limited, ISSN 1660-5373 DOI 10.1108/16605371011040889
Oscar Claveria is Assistant
Professor at the Research
Institute of Applied
Economics (IREA),
Department of
Econometrics, Statistics
and Spanish Economy,
University of Barcelona,
Barcelona, Spain.
Jordi Datzira is Consultor at
Datzira Development
Services, SL, Barcelona,
Spain.
Received 28 May 2009
Revised 31 August 2009
Accepted 23 September 2009
not to its magnitude. As pointed out by Pesaran (1987), this type of data are less likely to be
susceptible to sampling and measurement errors than surveys that require respondents to
give point forecasts. Statistical information from consumer surveys is available much more in
advance to quantitative statistics and is related with agents’ expectations. The fast
availability of the results and the wide range of variables covered make them very useful for
monitoring the current status of the economy, but there is no consensus on their utility for
forecasting macroeconomic developments.
The objective of the paper is to analyse the possibility of improving the forecasts for tourist
demand in Catalonia using the information provided by consumer surveys. As expansions
are more prolonged over time than recessions (Hansen, 1997), in the behaviour of most
economic variables there seems to be a cyclical asymmetry that linear models are not able
to capture. To overcome this issue, four different sets of models have been considered in the
paper: autoregressive (AR), autoregressive integrated moving average (ARIMA),
self-exciting threshold autoregressions (SETAR) and Markov switching regime (MKTAR)
models. Then the Root Mean Square Error (RMSE) has been computed for different forecast
horizons (one, two, three, six and 12 months).
In order to test if survey results provide useful information to improve forecasts of the tourism
demand in Catalonia we have considered the consumer confidence indicator (CCI) for the
four main visitor markets (France, the United Kingdom, Germany (see Appendix) and Italy)
from January 2002 to June 2008 and we have introduced as explanatory variable in
autoregressive (AR) and Markov switching regime (MKTAR) models, where the probability of
changing regime depends on the information of the qualitative indicators rather than on the
own evolution of the series. The comparison of these values with the ones obtained with
models where information from business and consumer would permit to assess whether
these indicators permit to improve the forecasts or not.
The structure of the paper is as follows. In the next section our methodological approach is
described, including both benchmark models and models where consumer surveys
information is included. Next, results of the forecasting competition are discussed in Section
3. Last, conclusions are given in Section 4.
2. Methodology
2.1 Benchmark models
A variety of time-series models have been used and compared to estimate and forecast
tourism demand. The most commonly used being exponential smoothing and
autoregressive integrated moving average (ARIMA) models (Li et al., 2005; Witt and Witt,
1995). In this work four different models (AR, ARIMA, SETAR and MKTAR models) have been
proposed to obtain forecasts for the quantitative variables expressed as year-on-year
growth rates. As there are few attempts in the literature to incorporate qualitative information
in quantitative forecasting models (Lee et al., 2006), AR models have also been applied
including qualitative survey data.
2.1.1 Autoregressions (AR). Autoregressions explain the behaviour of the endogenous
variable as a linear combination of its own past values:
x
t
¼
f
1
x
t21
þ ...
f
2
x
t21
þ ...þ
f
p
x
t2p
þ 1
t
ð1Þ
In order to determine the number of lags that should be included in the model, we have
selected the model with the lowest value of the Akaike Information Criteria (AIC) considering
models with a minimum number of 1 lag up to a maximum of 24 (including all the
intermediate lags).
2.1.2 Autoregressive integrated moving average models (ARIMA). The general expression
of an ARIMA model (Box and Jenkins, 1970) is the following:
x
l
t
¼
Q
s
L
s
ðÞ
u
LðÞ
F
s
L
s
ðÞ
u
LðÞD
D
s
D
d
1
t
ð2Þ
where Q
s
L
s
ðÞ¼1 2 Q
s
L
s
2 Q
2s
L
2s
2 ::: 2 Q
Qs
L
Qs
is a seasonal moving average
polynomial, F
s
L
s
ðÞ¼1 2 F
s
L
s
2 F
2s
L
2s
2 ::: 2 F
Ps
L
Ps
is a seasonal autoregressive
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polynomial,
u
LðÞ¼ 1 2
u
1
L
1
2
u
2
L
2
2 ::: 2
u
q
L
q
is a regular moving average polynomial,
and
f
LðÞ¼ 1 2
f
1
L
1
2
f
2
L
2
2 ::: 2
f
p
L
p
is a regular autoregressive polynomial,
l
is the
value of the Box and Cox (1964) transformation, D
D
s
is the seasonal difference operator, D
d
is
the regular difference operator, S is the periodicity of the considered time series, and 1
t
is the
innovation which is assumed to behave as a white noise. In order to use this kind of model
with forecasting purposes we have considered models with up to 12 AR and MA terms
selecting the model with the lowest value of the AIC.
2.1.3 Self-exciting threshold autoregressions models (SETAR). A self-excited threshold
autoregressive (SETAR) model (Hansen, 1997) for the time series x
t
can be summarised as
follows:
x
t
¼ BðLÞ · x
t
þ u
t
if x
t2k
# y ð3Þ
x
t
¼
z
ðLÞ · x
t
þ v
t
if x
t2k
. y ð4Þ
where u
t
and v
t
are white noises, B(L) and
z
(L) are autoregressive polynomials, the value k is
known as delay and the value y is known as threshold. This two-regime self-exciting
threshold autoregressive process is estimated and a Monte Carlo procedure is used to
generate multi-step forecasts. The selected values of the delay are those minimising the sum
of squared errors among values between 1 and 12. The values of the threshold are given by
the variation of the analysed variable.
2.1.4 Markov switching regime models (MKTAR). As an alternative to SETAR models, time
series regime-switching models assume that the distribution of the variable is known
conditional on a particular regime or state occurring. Hamilton (1989) presented the Markov
regime-switching model in which the unobserved regime evolves over time as a first order
Markov process. In this analysis, we use a Markov-switching threshold autoregressive model
(MKTAR) allowing for different regime-dependent intercepts, autoregressive parameters,
and variances. Once we have estimated the probabilities of expansion and recession using
the Hamilton filter together with the smoothing filter of Kim (1994), we construct the following
model for the time series x
t
using the estimated probabilities of changing regime:
x
t
¼ BðLÞ · x
t
þ u
t
if P Expansion = x
t2k
½# P ð5Þ
x
t
¼
z
ðLÞ · x
t
þ v
t
if P Expansion = x
t2k
½. P ð6Þ
where, u
t
and v
t
are white noises, B(L) and
z
(L) are autoregressive polynomials, k is the value
minimizing the sum of squared errors among 1 and 12 and the value P, known as threshold,
is given by the variation of the probability.
2.2 Models where consumer surveys information is incorporated
One way to use the qualitative information of survey data on the direction of change in order
to improve the forecasts of the quantitative variables consists in introducing selected
indicators as explanatory variables in autoregressions. Several recent works have estimated
autoregressive models for some target variable adding current and lagged values of a
consumer confidence index in order to test its significance and consider the extent of its
effects (Claveria et al., 2007; Easaw and Heravi, 2004; Vuchelen, 2004). We have followed
the same approach by incorporating the consumer confidence indicator (CCI) to
autoregressive (AR) models. We have excluded the rest of the benchmark models due to
the available data set.
The consumer confidence indicator (CCI) was designed by the European Commission in
order to summarise the results of the consumer surveys. This indicator is obtained as an
arithmetic mean of the answers (seasonal adjusted balances) to four questions:
CCI ¼ðQ
1
þ Q
2
þ Q
3
þ Q
4
þ Q
1
Þ = 4 ð7Þ
where Q
1
refers to the financial situation over the next 12 months, Q
2
to the general economic
situation over the next 12 months, Q
3
to the unemployment expectations over the next 12
months and Q
4
to the savings over the next 12 months.
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3. Results
Tourist data in this paper was obtained from Turisme de Catalunya and the Statistical
Institute of Catalonia (IDESCAT), as well as Frontur data from the Institute of Tourism Studies
(IET), while survey data from the European Commission. A descriptive analysis of this data
set can be found in Claveria and Datzira (2009).
In order to evaluate the relative forecasting accuracy, all models were estimated from
January 2002 to June 2007 and forecasts for one, two, three, six and 12 months ahead were
computed. The specifications of the models are based on information up to that date and,
then re-estimated each month for forecasts to be computed. Given the availability of actual
values until June 2008, forecast errors can be computed in a recursive way (i.e. for the 1
month forecast horizon, 12 forecast errors can be computed). All calculations are performed
with Gauss for Windows 6.0.
To summarise this information, the Root Mean Squared Error (RMSE) has been computed so
methods can be ranked according to their values. It is worth mentioning that in all cases we
have assumed that the information of business and consumer surveys is known in advance,
which is not a strong assumption for shorter forecasting horizons but it could be for longer
ones.
The results of our forecasting competition are shown in Tables I to IV. These tables
present the values of the Root of the Mean Squared Error (RMSE) obtained from recursive
forecasts for one, two, three, six and 12 months during the period 2007.06-2008.06 for
both, the benchmark models and the models including information from surveys. Each
table shows the average RMSE for each countr y for both the number of arrivals and the
overnight stays.
The obtained results permit to conclude that, as expected, forecasts errors increase for
longer horizons in most cases. Regarding the forecast accuracy of the different methods, in
most cases ARIMA models are not outperformed by the rest of the methods, being the
SETAR models the ones usually displaying the highest RMSE values. MKTAR models usually
show lower RMSE values than other methods, although they do not always converge due to
the available data. When information from consumer surveys is incorporated, AR models do
not seem to obtain lower RMSE than benchmark models.
In Table V we present the results for one moth ahead by country. In this case, ARIMA models
display the lowest RMSE values. While Germany is the country with lowest RMSE values for
all models except for SETAR models, Italy shows very high RMSE values. Summarising, the
Table I Average RMSE – France
1 month 2 months 3 months 6 months 12 months
Arrivals
Benchmark models
AR 6.66 13.44 16.60 18.29 21.17
ARIMA 2.56
a
4.66 5.82 8.31 10.66
SETAR 4.56 6.40 7.36 12.71 25.30
MKTAR
bbbbb
Models with survey information
AR 5.59 8.02 8.71 11.04 14.91
Overnight stays
Benchmark models
AR 17.12 18.14 17.44 20.21 6.04
a
ARIMA 7.95 7.58 7.76 10.73 7.45
SETAR 12.16 15.04 15.75 17.28 17.08
MKTAR
bbbbb
Models with survey information
AR 24.37 26.05 25.59 36.48 47.94
Notes:
a
Best model;
b
Matrix singular or not positive definite; Figures in italic are best model without
survey information
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comparison of the forecasting performance of the two sets of models permit to conclude that
in most cases, models that include information from the survey do not obtain lower RMSE
than the corresponding benchmark model without survey information.
4. Conclusions and discussion
Forecasting tourist demand using both quantitative forecasting models and qualitative
techniques has received limited attention in the literature. There is also a lack of studies on
tourism demand in Catalonia. Thus, the objective of the paper is to analyse the possibility of
Table II Average RMSE – UK
1 month 2 months 3 months 6 months 12 months
Arrivals
Benchmark models
AR 12.23 13.15 12.79 11.05 31.46
ARIMA 4.44
a
5.49 7.22 11.08 14.35
SETAR 12.10 24.22 39.85 51.89 74.87
MKTAR 7.52 8.08 10.43 4.75 5.18
Models with survey information
AR 9.91 13.61 16.52 21.81 16.26
Overnight stays
Benchmark models
AR 12.42 13.43 14.38 16.23 5.04
a
ARIMA 7.29 8.46 8.87 11.36 26.05
SETAR 248.71 641.07 2 507 19 252 19 629 900
MKTAR
bb b b b
Models with survey information 1
AR 13.78 13.71 18.25 25.46 21.52
Notes:
a
Best model;
b
Matrix singular or not positive definite; Figures in italic are best model without
survey information
Table III Average RMSE – Germany
1 month 2 months 3 months 6 months 12 months
Arrivals
Benchmark models
AR 3.78 4.55 4.98 5.97 9.47
ARIMA 1.88
a
2.55 2.56 3.82 9.23
SETAR 11.62 11.79 14.83 139.95 3 913.97
MKTAR 2.59 4.33 5.77 8.65 4.56
Models with survey information
AR 6.53 9.09 10.20 10.29 11.38
Overnight stays
Benchmark models
AR 4.23 4.58 4.72 5.43 3.52
a
ARIMA 4.15 5.78 6.85 8.53 12.13
SETAR 16.75 17.62 19.27 18.25 9.95
MKTAR
bbb b b
Models with survey information
AR 13.78 13.71 18.25 25.46 21.52
Notes:
a
Best model;
b
Matrix singular or not positive definite; Figures in italic are best model without
survey information
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improving the forecasts for tourist demand for Catalonia using the information provided by
consumer surveys.
Consumer surveys provide detailed information about agents’ expectations. The fact that
survey results are based on the knowledge of respondents operating in the market, and the
rapid availability of the results, make them very useful for monitoring the current state of the
economy. Therefore consumers’ expectations have become an essential tool for the making
of business decisions and the drawing up of tourist policies in periods of high uncertainty as
the present.
Taking into account that expansions are more prolonged over time than recessions, most
economic variables show a cyclical asymmetry that linear models are not able to capture. To
Table IV Average RMSE – Italy
1 month 2 months 3 months 6 months 12 months
Arrivals
Benchmark models
AR 21.44 25.50 28.43 27.81 38.44
ARIMA 8.64 9.15 7.69
a
8.59 23.46
SETAR 15.13 28.59 44.57 99.76 271.31
MKTAR
bb b bb
Models with survey information
AR 20.98 25.94 29.62 39.64 60.18
Overnight stays
Benchmark models
AR 70.84 85.77 81.26 77.14 102.83
ARIMA 63.05 64.17 65.11 76.35 47.57
a
SETAR 261.77 519.24 2 400.41 67 696.97 572.31
MK-TAR
bb b bb
Models with survey information
AR 55.86 63.72 65.82 63.52 99.80
Notes:
a
Best model;
b
Matrix singular or not positive definite; Figures in italic are best model without
survey information
Table V Summary of results by country – average RMSE for 1 month ahead
France UK Germany Italy
Arrivals
Benchmark models
AR 6.66 12.23 3.78 21.44
ARIMA 2.56 4.44 1.88
a
8.64
SETAR 4.56 12.10 11.62 15.13
MKTAR
b
7.52 2.59
b
Models with survey information
AR 5.59 9.91 6.53 20.98
Overnight stays
Benchmark models
AR 17.12 12.42 4.23 70.84
ARIMA 7.95 7.29 4.15
a
63.05
SETAR 12.16 248.71 16.75 261.77
MKTAR
bbb b
Models with survey information
AR 24.37 13.78 9.95 55.86
Notes:
a
Best model. The estimation results of the models are reported in the Appendix;
b
Matrix
singular or not positive definite; Figures in italic are best model without survey information
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overcome this issue, four different sets of models have been considered in the paper:
autoregressive (AR), autoregressive integrated moving average (ARIMA), self-exciting
threshold autoregressions (SETAR) and Markov switching regime (MKTAR) models. While
ARIMA models have been widely used in the tourism literature, non-linear models such as
SETAR and MKTAR are used for the first time to forecast tourist demand.
In order to test if survey results provide useful information to improve forecasts of the tourism
demand in Catalonia, the number of tourists and overnight stays has been forecasted for the
four main visitor markets (France, the United Kingdom, Germany and Italy), with and without
considering survey results. This forecasting competition has extended previous research
that has considered information from business and consumer surveys to explain the
behaviour of macroeconomic variables (Claveria et al., 2007; Vuchelen, 2004) to the tourist
demand literature.
When comparing the forecasting accuracy of the different techniques, ARIMA and Markov
switching regime models outperform the rest of the models. Forecasts of arrivals show lower
RMSEs than forecasts of overnight stays. To our surprise, the obtained results allow us to
conclude that only in a limited number of cases the consideration of information from
consumer surveys has improved the forecasting performance of the different models.
References
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Box, G.E.P. and Jenkins, G.M. (1970), Time-series Analysis: Forecasting and Control, Holden Day, San
Francisco, CA.
Claveria, O. and Datzira, J. (2009), ‘‘Tourism demand in Catalonia: detecting external economic
factors’’, Tourismos, Vol. 4, pp. 13-28.
Claveria, O., Pons, E. and Ramos, R. (2007 ), ‘‘Business and consumer expectations and
macroeconomic forecasts’’, International Journal of Forecasting, Vol. 23, pp. 47-69.
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Tourism Management, Vol. 27, pp. 773-80.
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Perspectives, Vol. 18, pp. 29-50.
Pesaran, M.H. (1987), The Limits to Rational Expectations, Basil Blackwell, Oxford.
Vuchelen, J. (2004), ‘‘Consumer sentiment and macroeconomic forecasts’’, Journal of Economic
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International Journal of Forecasting, Vol. 11, pp. 447-75.
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Appendix. Estimation results
The estimation results of the best models used for forecasting tourism demand in Catalonia
for one month ahead, corresponding to Germany for both arrivals and overnight stays, are
reported in Tables AI-AXII.
Table AI Estimation results for 1 month ahead (Germany) – estimation until 2007:06
Benchmark models ARIMA (8,1,9)
Estimation until observation 78 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 0.256 4.198 0.061 0.952
AR(2) 2 0.325 2.850 2 0.114 0.909
AR(3) 0.622 3.068 0.203 0.840
AR(4) 2 0.145 4.468 2 0.032 0.974
AR(5) 0.299 3.012 0.099 0.921
AR(6) 2 0.131 3.160 2 0.042 0.967
AR(7) 0.049 2.437 0.020 0.984
AR(8) 0.332 1.860 0.179 0.859
MA(1) 0.931
MA(2) 2 0.477
MA(3) 0.868
MA(4) 2 0.566
MA(5) 0.281
MA(6) 2 0.315
MA(7) 0.060
MA(8) 0.403
MA(9) 2 0.185
Overnight stays
AR(1) 0.282 9.014 0.031 0.975
AR(2) 2 0.794 1.838 2 0.432 0.668
AR(3) 0.111 7.471 0.015 0.988
AR(4) 2 0.517 0.536 2 0.965 0.338
AR(5) 0.402 4.807 0.084 0.934
AR(6) 2 0.610 3.126 2 0.195 0.846
AR(7) 0.429 5.397 0.079 0.937
AR(8) 0.006 3.521 0.002 0.999
MA(1) 0.823
MA(2) 2 0.774
MA(3) 0.461
MA(4) 2 0.243
MA(5) 0.584
MA(6) 2 0.550
MA(7) 0.753
MA(8) 2 0.010
MA(9) 2 0.043
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AII Estimation results for 1 month ahead (Germany) – estimation until 2007:07
Benchmark models ARIMA (8,1,9)
Estimation until observation 79 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 1.382 0.472 2 2.926 0.005
AR(2) 2 0.545 2.491 2 0.219 0.827
AR(3) 0.200 3.693 0.054 0.957
AR(4) 2 0.328 3.012 2 0.109 0.914
AR(5) 2 0.870 1.026 2 0.848 0.400
AR(6) 2 0.019 2.248 2 0.008 0.993
AR(7) 0.509 2.846 0.179 0.859
AR(8) 0.349 1.836 0.190 0.850
MA(1) 2 0.724
MA(2) 0.400
MA(3) 0.629
MA(4) 2 0.420
MA(5) 2 0.760
MA(6) 0.436
MA(7) 0.466
MA(8) 0.007
MA(9) 2 0.189
Overnight stays
AR(1) 2 0.234 0.768 2 0.305 0.761
AR(2) 2 0.998 0.470 2 2.123 0.038
AR(3) 0.086 0.976 0.088 0.930
AR(4) 2 0.727 0.434 2 1.674 0.099
AR(5) 0.237 0.713 0.332 0.741
AR(6) 2 0.259 0.406 2 0.639 0.525
AR(7) 0.264 0.340 0.774 0.442
AR(8) 2 0.406 0.441 2 0.920 0.361
MA(1) 0.326
MA(2) 2 0.696
MA(3) 0.665
MA(4) 2 0.433
MA(5) 0.658
MA(6) 2 0.028
MA(7) 0.495
MA(8) 2 0.332
MA(9) 0.342
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AIII Estimation results for 1 month ahead (Germany) – estimation until 2007:08
Benchmark models ARIMA (8,1,9)
Estimation until observation 80 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 1.387 3.022 2 0.459 0.648
AR(2) 2 0.995 3.767 2 0.264 0.792
AR(3) 2 0.090 3.950 2 0.023 0.982
AR(4) 2 0.897 3.146 2 0.285 0.777
AR(5) 2 1.177 3.324 2 0.354 0.725
AR(6) 2 0.518 3.842 2 0.135 0.893
AR(7) 0.402 3.363 0.120 0.905
AR(8) 0.276 2.469 0.112 0.911
MA(1) 2 0.704
MA(2) 2 0.029
MA(3) 0.630
MA(4) 2 0.812
MA(5) 2 0.653
MA(6) 0.205
MA(7) 0.691
MA(8) 2 0.026
MA(9) 2 0.228
Overnight stays
AR(1) 0.437 7.443 0.059 0.953
AR(2) 2 0.804 1.940 2 0.415 0.680
AR(3) 0.184 6.096 0.030 0.976
AR(4) 2 0.577 0.927 2 0.623 0.536
AR(5) 0.491 4.016 0.122 0.903
AR(6) 2 0.507 2.817 2 0.180 0.858
AR(7) 0.407 3.358 0.121 0.904
AR(8) 2 0.006 2.509 2 0.002 0.998
MA(1) 0.920
MA(2) 2 0.804
MA(3) 0.504
MA(4) 2 0.297
MA(5) 0.619
MA(6) 2 0.446
MA(7) 0.571
MA(8) 2 0.010
MA(9) 2 0.057
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AIV Estimation results for 1 month ahead (Germany) – estimation until 2007:09
Benchmark models ARIMA (8,1,9)
Estimation until observation 81 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.581 3.850 2 0.151 0.880
AR(2) 2 0.737 5.238 2 0.141 0.889
AR(3) 0.071 6.404 0.011 0.991
AR(4) 2 0.406 4.772 2 0.085 0.933
AR(5) 2 0.514 4.620 2 0.111 0.912
AR(6) 2 0.237 5.532 2 0.043 0.966
AR(7) 0.099 4.667 0.021 0.983
AR(8) 0.563 3.284 0.172 0.864
MA(1) 0.081
MA(2) 2 0.353
MA(3) 0.594
MA(4) 2 0.458
MA(5) 2 0.328
MA(6) 0.045
MA(7) 0.168
MA(8) 0.561
MA(9) 2 0.361
Overnight stays
AR(1) 0.394 11.039 0.036 0.972
AR(2) 2 0.853 2.452 2 0.348 0.729
AR(3) 0.183 9.379 0.020 0.985
AR(4) 2 0.548 0.814 2 0.674 0.503
AR(5) 0.428 5.866 0.073 0.942
AR(6) 2 0.446 3.500 2 0.127 0.899
AR(7) 0.441 4.450 0.099 0.921
AR(8) 2 0.036 4.191 2 0.009 0.993
MA(1) 0.884
MA(2) 2 0.843
MA(3) 0.530
MA(4) 2 0.258
MA(5) 0.536
MA(6) 2 0.334
MA(7) 0.574
MA(8) 2 0.057
MA(9) 2 0.033
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AV Estimation results for 1 month ahead (Germany) – estimation until 2007:10
Benchmark models ARIMA (8,1,9)
Estimation until observation 82 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.776 21.478 2 0.036 0.971
AR(2) 2 0.766 31.160 2 0.025 0.980
AR(3) 2 0.034 36.995 2 0.001 0.999
AR(4) 2 0.197 25.394 2 0.008 0.994
AR(5) 2 0.536 20.667 2 0.026 0.979
AR(6) 2 0.253 25.272 2 0.010 0.992
AR(7) 2 0.057 22.091 2 0.003 0.998
AR(8) 0.495 16.080 0.031 0.976
MA(1) 2 0.117
MA(2) 2 0.260
MA(3) 0.521
MA(4) 2 0.144
MA(5) 2 0.484
MA(6) 0.017
MA(7) 0.009
MA(8) 0.558
MA(9) 2 0.274
Overnight stays
AR(1) 0.181 11.150 0.016 0.987
AR(2) 2 0.728 1.758 2 0.414 0.680
AR(3) 0.061 8.570 0.007 0.994
AR(4) 2 0.475 0.615 2 0.773 0.443
AR(5) 0.377 5.401 0.070 0.945
AR(6) 2 0.463 3.949 2 0.117 0.907
AR(7) 0.415 5.156 0.081 0.936
AR(8) 0.018 4.608 0.004 0.997
MA(1) 0.697
MA(2) 2 0.654
MA(3) 0.371
MA(4) 2 0.183
MA(5) 0.538
MA(6) 2 0.402
MA(7) 0.672
MA(8) 2 0.007
MA(9) 2 0.032
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AVI Estimation results for 1 month ahead (Germany) – estimation until 2007:11
Benchmark models ARIMA (8,1,9)
Estimation until observation 83 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.026 5.986 2 0.004 0.997
AR(2) 0.093 3.009 0.031 0.976
AR(3) 0.534 1.892 0.282 0.779
AR(4) 2 0.121 3.485 2 0.035 0.972
AR(5) 0.023 3.506 0.007 0.995
AR(6) 0.127 2.142 0.059 0.953
AR(7) 0.094 1.571 0.060 0.952
AR(8) 0.256 1.529 0.168 0.867
MA(1) 0.637
MA(2) 0.137
MA(3) 0.486
MA(4) 2 0.462
MA(5) 2 0.040
MA(6) 0.107
MA(7) 2 0.034
MA(8) 0.278
MA(9) 2 0.108
Overnight stays
AR(1) 0.519 3.776 0.137 0.891
AR(2) 2 0.895 1.646 2 0.544 0.588
AR(3) 0.237 3.763 0.063 0.950
AR(4) 2 0.558 0.743 2 0.751 0.456
AR(5) 0.519 2.051 0.253 0.801
AR(6) 2 0.420 1.416 2 0.297 0.767
AR(7) 0.425 1.607 0.265 0.792
AR(8) 0.015 1.614 0.009 0.993
MA(1) 1.007
MA(2) 2 0.962
MA(3) 0.569
MA(4) 2 0.298
MA(5) 0.592
MA(6) 2 0.334
MA(7) 0.513
MA(8) 0.003
MA(9) 2 0.090
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AVII Estimation results for 1 month ahead (Germany) – estimation until 2007:12
Benchmark models ARIMA (8,1,9)
Estimation until observation 84 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 0.248 4.460 0.056 0.956
AR(2) 2 0.764 1.969 2 0.388 0.699
AR(3) 2 0.201 3.650 2 0.055 0.956
AR(4) 2 0.806 3.513 2 0.229 0.819
AR(5) 0.047 4.411 0.011 0.991
AR(6) 2 0.389 2.732 2 0.142 0.887
AR(7) 2 0.317 2.438 2 0.130 0.897
AR(8) 0.199 3.149 0.063 0.950
MA(1) 0.917
MA(2) 2 0.930
MA(3) 0.310
MA(4) 2 0.653
MA(5) 0.473
MA(6) 2 0.349
MA(7) 2 0.161
MA(8) 0.485
MA(9) 2 0.175
Overnight stays
AR(1) 2 0.317 0.890 2 0.356 0.723
AR(2) 2 1.105 0.549 2 2.013 0.048
AR(3) 2 0.090 1.124 2 0.080 0.936
AR(4) 2 0.694 0.465 2 1.491 0.141
AR(5) 0.342 0.676 0.506 0.615
AR(6) 2 0.170 0.528 2 0.321 0.749
AR(7) 0.442 0.310 1.427 0.159
AR(8) 2 0.320 0.633 2 0.505 0.615
MA(1) 0.228
MA(2) 2 0.767
MA(3) 0.505
MA(4) 2 0.322
MA(5) 0.810
MA(6) 2 0.040
MA(7) 0.659
MA(8) 2 0.372
MA(9) 0.298
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AVIII Estimation results for 1 month ahead (Germany) – estimation until 2008:01
Benchmark models ARIMA (8,1,9)
Estimation until observation 85 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.178 2.002 2 0.089 0.929
AR(2) 2 0.800 2.025 2 0.395 0.694
AR(3) 2 0.124 2.555 2 0.049 0.961
AR(4) 2 0.739 2.217 2 0.333 0.740
AR(5) 2 0.327 2.286 2 0.143 0.887
AR(6) 2 0.347 2.428 2 0.143 0.887
AR(7) 2 0.187 2.019 2 0.092 0.927
AR(8) 0.337 1.828 0.184 0.854
MA(1) 0.497
MA(2) 2 0.674
MA(3) 0.408
MA(4) 2 0.674
MA(5) 0.071
MA(6) 2 0.104
MA(7) 2 0.066
MA(8) 0.530
MA(9) 2 0.278
Overnight stays
AR(1) 2 0.184 0.903 2 0.204 0.839
AR(2) 2 1.041 0.479 2 2.175 0.033
AR(3) 0.186 1.192 0.156 0.876
AR(4) 2 0.734 0.445 2 1.652 0.103
AR(5) 0.371 0.804 0.461 0.646
AR(6) 2 0.202 0.488 2 0.414 0.680
AR(7) 0.299 0.332 0.899 0.372
AR(8) 2 0.368 0.499 2 0.737 0.464
MA(1) 0.344
MA(2) 2 0.816
MA(3) 0.740
MA(4) 2 0.531
MA(5) 0.738
MA(6) 2 0.043
MA(7) 0.429
MA(8) 2 0.297
MA(9) 0.275
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AIX Estimation results for 1 month ahead (Germany) – estimation until 2008:02
Benchmark models ARIMA (8,1,9)
Estimation until observation 86 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.288 1.068 2 0.270 0.788
AR(2) 2 0.522 0.892 2 0.585 0.561
AR(3) 0.415 1.120 0.371 0.712
AR(4) 2 0.329 1.255 2 0.262 0.794
AR(5) 2 0.273 1.221 2 0.223 0.824
AR(6) 2 0.015 1.072 2 0.014 0.989
AR(7) 0.384 0.833 0.461 0.646
AR(8) 0.675 0.950 0.711 0.480
MA(1) 0.381
MA(2) 2 0.322
MA(3) 0.771
MA(4) 2 0.611
MA(5) 2 0.153
MA(6) 0.173
MA(7) 0.317
MA(8) 0.501
MA(9) 2 0.471
Overnight stays
AR(1) 2 0.125 0.872 2 0.144 0.886
AR(2) 2 1.024 0.493 2 2.079 0.041
AR(3) 0.151 1.066 0.142 0.888
AR(4) 2 0.644 0.425 2 1.517 0.134
AR(5) 0.404 0.726 0.556 0.580
AR(6) 2 0.242 0.446 2 0.542 0.590
AR(7) 0.365 0.285 1.283 0.204
AR(8) 2 0.357 0.498 2 0.718 0.476
MA(1) 0.447
MA(2) 2 0.776
MA(3) 0.657
MA(4) 2 0.400
MA(5) 0.771
MA(6) 2 0.181
MA(7) 0.559
MA(8) 2 0.354
MA(9) 0.277
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AX Estimation results for 1 month ahead (Germany) – estimation until 2008:03
Benchmark models ARIMA (8,1,9)
Estimation until observation 87 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 2 0.229 1.640 2 0.139 0.890
AR(2) 2 0.617 1.552 2 0.398 0.692
AR(3) 0.149 1.848 0.080 0.936
AR(4) 2 0.211 1.842 2 0.115 0.909
AR(5) 2 0.104 1.355 2 0.077 0.939
AR(6) 2 0.112 1.303 2 0.086 0.932
AR(7) 0.109 1.063 0.103 0.918
AR(8) 0.490 1.089 0.450 0.654
MA(1) 0.433
MA(2) 2 0.456
MA(3) 0.580
MA(4) 2 0.281
MA(5) 2 0.074
MA(6) 2 0.050
MA(7) 0.060
MA(8) 0.454
MA(9) 2 0.307
Overnight stays
AR(1) 2 0.456 0.850 2 0.536 0.594
AR(2) 2 1.074 0.683 2 1.573 0.120
AR(3) 2 0.139 1.095 2 0.127 0.899
AR(4) 2 0.689 0.475 2 1.451 0.151
AR(5) 0.349 0.632 0.553 0.582
AR(6) 2 0.066 0.535 2 0.123 0.903
AR(7) 0.459 0.393 1.167 0.247
AR(8) 2 0.308 0.680 2 0.453 0.652
MA(1) 0.067
MA(2) 2 0.709
MA(3) 0.509
MA(4) 2 0.353
MA(5) 0.856
MA(6) 0.030
MA(7) 0.685
MA(8) 2 0.438
MA(9) 0.322
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Table AXI Estimation results for 1 month ahead (Germany) – estimation until 2008:04
Benchmark models ARIMA (8,1,9)
Estimation until observation 88 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 0.207 2.533 0.082 0.935
AR(2) 2 0.440 1.966 2 0.224 0.824
AR(3) 0.404 1.474 0.274 0.785
AR(4) 2 0.557 1.815 2 0.307 0.760
AR(5) 0.140 2.155 0.065 0.948
AR(6) 0.010 1.601 0.006 0.995
AR(7) 0.292 1.616 0.181 0.857
AR(8) 0.396 1.892 0.209 0.835
MA(1) 0.890
MA(2) 2 0.578
MA(3) 0.684
MA(4) 2 0.838
MA(5) 0.399
MA(6) 2 0.021
MA(7) 0.191
MA(8) 0.294
MA(9) 2 0.309
Overnight stays
AR(1) 2 0.468 0.822 2 0.570 0.571
AR(2) 2 1.065 0.644 2 1.653 0.103
AR(3) 2 0.185 1.024 2 0.181 0.857
AR(4) 2 0.699 0.452 2 1.546 0.127
AR(5) 0.274 0.608 0.451 0.654
AR(6) 2 0.068 0.504 2 0.135 0.893
AR(7) 0.444 0.363 1.223 0.225
AR(8) 2 0.277 0.647 2 0.429 0.669
MA(1) 0.048
MA(2) 2 0.688
MA(3) 0.456
MA(4) 2 0.337
MA(5) 0.767
MA(6) 0.077
MA(7) 0.681
MA(8) 2 0.386
MA(9) 0.314
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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Corresponding author
Oscar Claveria can be contacted at: oclaveria@ub.edu
Table AXII Estimation results for 1 month ahead (Germany) – estimation until 2008:05
Benchmark models ARIMA (8,1,9)
Estimation until observation 89 Coefficients Std prob. Errors t-ratio
Arrivals
AR(1) 0.050 1.392 0.036 0.972
AR(2) 2 0.739 1.301 2 0.568 0.572
AR(3) 0.127 1.401 0.090 0.928
AR(4) 2 0.665 1.457 2 0.457 0.649
AR(5) 2 0.048 1.509 2 0.032 0.975
AR(6) 2 0.275 1.388 2 0.198 0.844
AR(7) 0.057 1.163 0.049 0.961
AR(8) 0.388 1.199 0.324 0.747
MA(1) 0.736
MA(2) 2 0.781
MA(3) 0.604
MA(4) 2 0.770
MA(5) 0.287
MA(6) 2 0.203
MA(7) 0.112
MA(8) 0.416
MA(9) 2 0.328
Overnight stays
AR(1) 2 0.415 0.807 2 0.514 0.609
AR(2) 2 1.023 0.689 2 1.484 0.142
AR(3) 2 0.089 1.045 2 0.085 0.932
AR(4) 2 0.650 0.493 2 1.319 0.191
AR(5) 0.386 0.605 0.637 0.526
AR(6) 2 0.080 0.499 2 0.161 0.873
AR(7) 0.420 0.376 1.117 0.268
AR(8) 2 0.383 0.619 2 0.618 0.539
MA(1) 0.101
MA(2) 2 0.690
MA(3) 0.500
MA(4) 2 0.361
MA(5) 0.886
MA(6) 2 0.028
MA(7) 0.651
MA(8) 2 0.533
MA(9) 0.364
Notes: The standard errors for the MA parameters are not reported because there is a MA root on the
boundary. The parameter estimates remain valid
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