Accuracy of econometric forecasts of tourism

Annals oj Eurrsm Raearch, Vol. 16, pp. 407-428, 1989 Printed in the USA. All rights reserved. Copyright

0

1989 Maxwell

Pergamon

0160.7383/89 $3.00 + .OO Macmillan plc and J. Jafarl

ACCURACY OF ECONOMETRIC FORECASTS OF TOURISM Christine A. Martin University of Bradford, UK University

College

Stephen F. Witt of Swansea, UK

Abstract: Many papers present estimated econometric models of international tourism demand. Their authors often suggest that these may be used for short-term forecasting, but actual forecasts are rarely provided. This paper presents the results of a study in which the forecasting accuracy of several quantitative techniques is compared. Statistically significant differences in accuracy are identified using the ANOVA and Scheffk tests. Several of the simple methods produce more accurate forecasts than econometrics; this finding is supported by an examination of the accuracy of commercially available econometric forecasts of tourism, where the naive “no change” model forecasts more accurately in 70% of cases. Keywords: forecasting international tourism demand, evaluation of forecasting accuracy, econometric models, time series models, ANOVA, Scheff.6 test. R&umC: L’exactitude des pr&isions &onomiques du tourisme. Beaucoup d’articles pr5sentent des modtles &onomCtriques de la demande touristique internationale. Les auteurs sugggrent souvent que l’on peut utiliser ces modtles pour des p&visions 2 courte terme, mais on fournit rarement des prtvisions concr&es. Le present article contient les r&ultats d’une &ude dans laquelle on compare le degr6 d’exactitude de plusieurs m5thodes de pr&ision quantitative. On discerne des diffgrences qui sont statistiquement signifiantes en employant des tests ANOVA et Scheff6. Plusieurs des mtthodes simples produisent des r&ultats plus exacts que ne font les mtthodes Cconom&riques; cette conclusion est appuy6e par une &ude de l’exactitude des p&visions &onom&riques du tourisme qui sont vendues commercialement, et oti le modsle nai’f “sans changement” produit des pr&isions plus exactes dans 70 pour cent des cas. Mots-cl&: prCvision de la demande touristique internationale, evaluation de l’exactitude de la pr&ision, modhles Cconomttriques, modkles de skries temporelles, ANOVA, test Scheffk.

INTRODUCTION It is generally accepted that forecasting tourism planning process. For example, need for forecasts in tourism:

plays an essential role in the Archer (1987:77) stresses the

Christine Martin (University of Bradford Management Centre, Emm Lane, Bradford, West Yorkshire, BD9 4JL, UK) lectures on operations management. Her research interests center on demand forecasting in tourism and operations management in the service industries. Stephen Witt is Lewis Professor of Tourism Studies. His research interests center on demand forecasting, econometric model-building, economic impact studies, and financial management. 407

408

ECONOMETRIC

FORECASTS

OF TOURISM

Forecasting should be an essential element in the process of management. No manager can avoid the need for some form of forecasting: a manager must plan for the future in order to minimize the risk of failure or, more optimistically, to maximize the possibilities of success. In order to plan, he must use forecasts Forecasts are needed for marketing, production, and financial planning.

A broad range of forecasting techniques is already available (Archer 1976, 1980, 1987; Calantone, Di Benedetto and Bojanic 1987; Duke 1981; Sheldon and Var 1985; Uysal and Crompton 1985; Vanhove 1980; World Tourism Organization 1978). In choosing from these techniques, the tourism manager will consider various attributes such as accuracy of the forecasts generated, ease of use of the forecasting technique, cost of producing the forecasts, and speed with which the forecasts can be produced. It is widely accepted, however, that accuracy is the most important characteristic of a forecast. According to Archer (1987:77), the accuracy of the forecasts will affect the quality of the management decision In the tourism industry, in common with most other service sectors, the need to forecast accurutely is especially acute because of the perishable nature of the product. Unfilled airline seats and unused hotel rooms cannot be stockpiled (emphasis added). In the field of forecasting

generally,

Makridakis

(1986:

15) notes that:

Improving the accuracy of forecasting involves considerable benefits for decision and policy makers who must use its prediction for planning, strategy and other types of future oriented decision making (emphasis added). Klein

(1984:

1) a 1so stresses

the importance

of accuracy:

the forecast itself has an intrinsic importance Its accuracyis the “bottom line” for the professional forecaster, much as the net profit is the ubottom line” for the chief executive of an enterprise (emphasis added). Many studies examine the demand for international tourism (see, for 1981; Loeb 1982; example, Gray 1966; Joseph and Jud 1974; Kliman Martin and Witt 1987, 1988; Uysal and Crompton 1984; Witt 1980a, 1980b; Witt and Martin 1987). Although such studies often suggest that the econometric models developed may be used for forecasting purposes, the models are not generally used to generate forecasts which are then evaluated in terms of accuracy. As Van Doorn (1982: 164) points out: Despite the growing file of reports on tourism forecasting, surprisingly little attention is paid to the comparison of actual data with the corresponding forecasts. This paper compares the accuracy of econometric forecasts of international tourism demand with the accuracy of forecasts obtained using six relatively simple univariate time series methods. Given the consid-

MARTIN

AND WITT

409

erable time and effort necessary for the development of econometric models, it would be expected that there would be a corresponding improvement in the accuracy of forecasts generated by these models compared with the forecasts generated by the univariate methods. The relative accuracy of the various methods is assessed, employing different measures of accuracy and different time horizons. Models are developed to forecast the following tourist flows: France to Italy, Morocco, Portugal, Spain, Switzerland and UK; Federal Republic of Germany (FRG) to Austria, France, Italy, Spain, Switzerland and Yugoslavia; UK to Austria, France, FRG, Greece, Italy and Spain; and USA to Canada, France, FRG, Italy, Mexico and UK. The data used in the study are annual and for outward tourism from France and FRG cover the period 1965 to 1983, from USA the period 1965 to 1984, and from UK the period 1965 to 1985 (the most recent data available at the time the analysis was carried out). Finally, the paper compares the results obtained in this study with the forecasting ability of the econometric model (TRAM) developed by Coopers and Lybrand to forecast travel flows from USA (see Means and Avila 1986, 1987). These econometric forecasts are published by the American Express Publishing Corporation in the World Eauel Ouerview. This paper assesses the accuracy of these econometric forecasts relative to the accuracy of forecasts generated by the random walk “no change” model. FORECASTING

TESTS

Within Sam@ Le/Outsi& Sample Several authors examine forecasting ability on the basis of model fit, that is within sample forecasts are calculated (cf. Kunst and Neusser 1986). However, such a procedure is likely to give a flattering impression of a model’s ability to forecast accurately. Out of sample forecasting represents the situation faced by the forecaster in reality and is also a more stringent test. Thus Fildes (1985:552) states that only empirical outsidesample comparisonswill be given full weight it is all too easy to develop theoretically attractive models and then find data to fit them. What is more difficult is to develop models that can withstand the rigours of being tested on fresh data. This study, therefore, concentrates on out of sample forecasting ability. The various forecasting models are estimated over the periods 1965-80, 1965-81, and 1965-82 for all origins, 1965-83 for UK and USA, and 1965-84 for UK. These models are used to generate forecasts of tourist flows for one and two years ahead, with the exception of the final models which are only used to predict one year ahead. Thus sets of oneyear-ahead and two-years-ahead forecasts are generated for each origin. Measures of Accuracy In order

to examine

the accuracy

of the forecasting

methods

under

410

ECONOMETRIC

FORECASTS

OF TOURISM

consideration, it is necessary to select a particular measure of accuracy. As the forecasting tests are carried out on data series of origin-destination tourist flows of widely differing sizes, it is essential to use a criterion of forecast accuracy which is measured in unit free terms. In this study, two measures of accuracy, mean absolute percentage error (MAPE) and root mean square percentage error (RMSPE), are used in all the comparisons of forecasting methods. Thus, results are presented for each accuracy criterion. As there is some justification for each criterion, it is interesting to examine the extent to which the two criteria produce consistent results. Although the use of MAPE is widely Lawrence, Edmundson, and O’Connor 1985) many supported (e.g., authors consider that an accuracy criterion specified in terms of squared errors is often more appropriate than one in terms of absolute errors (cf. Meade and Smith 1985; Theil 1966); thus, RMSPE is also examined. The error (e) is defined as e, = t, -

v,

(1)

where V, denotes the number of tourist visits in period the forecast value. If there are n forecasts, then

MAPE=$&

t and

,. V, denotes

100

n,=, v, where

1e, 1 denotes

the absolute

RMSPE=

FORECASTING

value of the error.

(3)

METHODS

Econometrics Separate models are constructed for each origin-destination pair and potential explanatory variables include origin income, the cost of living for tourists in the destination, the cost of living for tourists in substitute destinations, the cost of travel between the origin and destination, the cost of travel between the origin and substitute destinations, the exchange rate between the currencies of the origin and destination, oil crisis dummy variables, a foreign currency restriction dummy variable, a lagged dependent variable, and a trend term. (For a full discussion of the justification and data sources for the explanatory variables, see Martin and Witt 1988.) The basic model is specified in log-linear form as follows:

MARTIN

In+=a,+a,

11

AND WITT

In ?+a,

In C,,+cq In CS,,

+c~, In EXil+ol, In TA,,+(r, In TAS,, +a, In TSg,+ag In TSSt,,+a,,, DVl, +o,,DI,‘&-fc@I,‘3,,+

t=1.2

aI,

a2,

, .

.

. >16(1=1965,

411

uqt

(4)

. ,16=1980)

is the number of tourist visits from origin i to destinationj in year t is the origin i population in year t is personal disposable income in origin i in year t (1980 prices) is the cost of living for tourists in destinationj in year t (1980 prices) is a weighted average of the cost of tourism in substitute destinations for residents of origin i in year t (1980 prices) is the rate of exchange between the currencies of origin i and destinationj in year t is the cost of travel by air from origin i to destinationj in year t (1980 prices) is a weighted average of the cost of travel by air to substitute destinations from origin i in year t (1980 prices) is the cost of travel by surface from origin i to destinationj in year t (1980 prices) is a weighted average of the cost of travel by surface to substitute destinations from origin i in year t is a dummy variable which picks up the effects of the 1974 oil crisis DVll=l ift=lO (1974) or 11 (1975) = 0 otherwise is a dummy variable which picks up the effects of the 1979 oil crisis DE?,=1 ift=15 (1979) = 0 otherwise is a dummy variable which picks up the effects of the 1967-69 UK currency restrictions (applies to UK origin models only) DIG,,=1 if i refers to the UK and t=3 (1967), 4 (1968) or 5 (1969) = 0 otherwise is a random disturbance term and are unknown parameters. . . , aI2

In addition, a trend term aY,,t and/or lagged dependent variable term in the model for those origin-destinaa,,ln ( ~l~,~I~~~~t_IJ is incorporated tion pan-s where the preliminary empirical results indicated that this may be necessary. The procedure adopted for selecting a “best” model for each origindestination pair is described in Martin and Witt (1988). As an example, Table 1 shows the models estimated for tourism flows from UK to

ECONOMETRIC

412

FORECASTS

Table 1. Best Models Explanatory Variable

OF TOURISM

for UK Outward

Tourism

Drstination Germany Greere

France

-47.819 (-38.51P

-18.619 (-6.12)a

-20.482 (-7.81P

-28.863 (-3.03P

.37.017 I-11.87P

-23.563 1.4.2lP

4.660 (24.OOP

1.952 14.26P

2.387 (6.16P

0.387 10.31)

4.394 (10.63P

1.775 (1.97)

-0.236 1-1.60)

-0.946 (-6.50)a

-0.361 (-1.75)

-5.605 I-8.59P

-1.608 (-7.64P

1IlCS

0.130 wz31

1.410 (5.64P

1nEX

1.659 (6.62P

Constant

Italy

Spain

Austria

Y InP 1nC

0.637 (1.18)

1nTA 1nTAS

0.540 (3.03P

0.492 (1.07)

-1.7fi5 (-3.73P

-0.394 f-0.41)

-0.081 (-0.83)

5.069 15.2lP

1nTSS DVl

-0.268 f-10.64P

DV2

-0.619 (-10.23P

DV3

-0.061 (-2.82P

-0.265 (-4.27P

-0.264 (-4.b3P

252.16

166.85

(1. IU) -0.179 (-4.43P

-0.111 (-11.42)0

19.46

106.69

33.37

R2

,983

,968

.803

.969

,869

R2

,991

.977

,095

,976

,913

DW COlOLS

-0.022 (-0.26)

-0.052 f-1.60) 0.056 (2.82P

TREND F

-0.420 (-3.lz)a

26.79 ,840 ,911

2.34

2.13

1.95

1.68

2.38

1.73

co

co

co

co

co

co

The figures in brarkets arc t values. a indicates significant at 6% level.

the six destinations considered. It can be seen that as measured by conventional criteria, good empirical results are obtained, thus providing support for the set of explanatory variables chosen. For example, many of the hypothesized explanatory variables have statistically significant impacts on tourist flows and high levels of goodness-of-fit are generally achieved. Naive 1 The period

forecast t:

for period

t + 1 is equal to the actual

q+,=v,.

number

of visits in

(5)

Naiue 2 The forecast for period t + 1 is equal to the actual number of visits in period t multiplied by the growth rate over the previous period:

MARTIN AND WITT

413

(6)

Exponential Smoothing Some of the origin-destination pair data series contain trends. Hence, an appropriate form of exponential smoothing is Brown’s one parameter double exponential smoothing model (Brown 1963). Where this technique reduces to single exponential no trend is present, smoothing.

Trend Curve Analysis Ten linear equation trend curves are fitted to each data series and the curve exhibiting the best fit is selected to generate the forecasts. The trend curves comprise linear, constrained hyperbola, exponential, geometric, semilog, modified exponential, hyperbola, modified hyperbolic, quadratic and log quadratic: Linear Constrained

Hyperbola

t=a+/3,t

(7)

+a+&~

(8)

t

1

Exponential

t

e=cr+P,ln

Semilog Exponential

t

Hyperbolic

Quadratic Log Quadratic

(11)

t

+=a+p,t t=a+p,t+P,t* In ~=a+P,t+&P

where (II, /3,, p2 are parameters to be estimated, t represents the time period.

(10)

(12)

In <=u+/3,!

q=cY+p,i t

Hyperbola

Modified

(9)

lnt=cr+/3,ln

Geometric

Modified

In t=a+@,t

and

(13)

(14) (15) (16)

414

ECONOMETRIC

FORECASTS

OF TOURISM

Table 2 shows, as an illustration, the form of trend curve selected for each origin-destination pair for the estimation period 1965-81. It can be seen that by far the most popular curve is log quadratic (67% of and modified hyperbolic (4%). cases), followed by quadratic (29%) None of the other seven curve types is featured. For the other estimation periods, only the log quadratic and quadratic curves appeared.

Gompertz This S-shaped curve is often used to represent the pattern of a product life cycle, and is estimated using nonlinear estimation techniques. Given the popularity of and theoretical justification for the product life cycle concept, it was decided specifically always to include this particular form of trend curve in the forecasting comparisons.

Stepwise Autoregression The

autoregressive

model

takes the form:

(17) where (Y, &, fi,, 0, are parameters

to be estimated.

A stepwise process based on incremental F Statistics is used to determine whether a variable is added to or removed from (17) until the coefficients of each variable in the equation are statistically significant at the 5% level. (In a few instances, no acceptable autoregressive model was estimateda statistically significant coefficient could not be obtained for any of the potential explanatory variables - and, hence, forecasts were not generated.)

Table 2. Form of Trend Curve

Fl%WlC~

Dent.innt.inns Austria Canada FWllW2 FRG Greece ltaly Mexico MWOCCCI Portugal Spain ;,p-rlsnd Yugoslavia Note:

The numbers

for 1965-8 origins

FRG

UK

16

14

16 15

15

16 16 16 16

16 16 16

16

16

16

refer to the equations

Selected

in the text.

15 16

1

USA

:: 16 16 16

16

MARTIN

EX ANTE/EX

AND WITT

415

POST

In the ex an& approach to forecasting, no advantage is taken of any information which would not have been available to a forecaster at the point in time from which forecasts are generated. This type of forecasting is more stringent than the ex post approach, where information which subsequently becomes available is used to generate forecasts. (For example, in econometric forecasting, known values of the explanatory variables may be used to provide forecasts of the dependent variable.) The ex ante approach is, therefore, adopted in all cases other than for econometric forecasting. By using expost forecasts for the econometric method, it has to some extent an unfair advantage over the other methods. In practice, it is unlikely that econometric forecasts will have the same degree of accuracy as those presented here, and this point should be borne in mind when the accuracy comparisons are made (although this is not necessarily the case; see Fildes 1985:571-72). However, it proved necessary to adopt the expost approach for the econometric method on account of the difficulties involved in obtaining generally accepted retrospective forecasts of some of the explanatory variables, in particular forecasts of fares. Furthermore, by using ex post forecasts for the econometric method, the forecast errors relate directly to the forecasting technique rather than also incorporating those errors arising from inaccurate forecasts of the explanatory variables. DATA DEFINITIONS

AND SOURCES

In the case of France, the data relate to holidays, plus visits to friends and relatives (minimum four days), and were obtained from L’Economie du Tourisme (Ministere du Commerce Exterieur et du Tourisme) and Annuaire Statistique de la France (Institut National de la Statistique et des Etudes Economiques). German data refer to holidays, plus visits to friends and relatives (minimum five days), and are published by the Statistisches Bundesamt in Fachserie 8 Reihe 8, Sonderbeitrag Urlaubs- und Erhlungsreisen. For UK, the data refer to holidays only (minimum one night) and were supplied by the Department of Trade and Industry. In the case of USA, the figures relate to holidays, visits to friends and relatives, and business visits (minimum one night), and were obtained from several sources. Statistics Canada provided the data on travel to Canada, the Banco de Mexico and Ministry of Tourism in Mexico supplied the data on travel to Mexico, and the remaining data are published in the Survey of Current Busies (U.S. Department of Commerce). For certain origin/destination pairs, there were missing observations in some years and it was necessary to use supplementary data obtained from destination National Tourist Offices. FORECASTING

PERFORMANCE

Tables 3 and 4 summarize the performance of the seven forecasting methods across the various origin countries for both one-year-ahead and two-years-ahead forecasting horizons. Table 3 shows the results for MAPE and Table 4 for RMSPE.

416

ECONOMETRIC

FORECASTS

OF TOURISM

Table 3. Forecasting Performance (MAPE) by Forecasting Method, Origin Country, and Forecasting Horizon Forecaasting Horizon IYw5) 1

Origin Country

Forecasting Method

Fl?NWe

FRG

UK

USA

Econometrics

10.98 (31

11.28 (7)

20.91 (5)

12.36 (2)

5.80 (1)

12.73 (1)

11.94 (1)

10.55 (6)

15.73 (2)

14.10 14)

Naive

1

9.06 Ill

Naive

2

12.76 16)

Exponential Smoothing

2

Note:

Figures

9.38 (2)

7.29 (3)

16.72 (4)

12.96 (3)

Gompertz

13.41 (6)

9.07 (5)

24.12 171

16.48 (6)

Trend Curve Analysis

12.54 (4)

8.33 (4)

22.12 (6)

20.93 (71

Autoregression

13.45 (7)

5.96 12)

15.81 (3)

15.03 (51

Econometrics

14.07 14)

16.36 (6)

26.00 (4)

11.27 (2)

Naive 1

10.08 (2)

7.69 12)

18.24 (2)

19.43 (4)

Naive 2

22.13 (7)

20.77 171

29.42 (5)

17.34 (3)

Exponential Smoothing

10.22 (3)

12.17 (4)

23.24 (3)

20.48 (6)

Gompertz

16.46 (51

13.03 (bi

30.46 (7)

21.19 IF)

Trend Curve Analysis

17.41 (6)

10.61 (31

30.04 (6)

29.56 17)

Autoregression

10.04 (11

6.10 (1)

16.76 (1)

10.73 (11

in brackets

denote

rankings

Naive 1, the “no change” model, has the lowest MAPE and lowest RMSPE of all the forecasting methods for each of the origin countries, France, FRG, UK, and USA, when one-year-ahead forecasts are considered. On moving to two-years-ahead forecasts, however, naive 1 only comes in first position once. For all other two-years-ahead forecasts, autoregression performs best. International tourism demand does change over time, and while a “no change” (minimum information) forecast may prove adequate over a one-year time horizon, improved forecasting can generally be achieved over a two-year time horizon by taking the dynamics of a time series into account. (For a longer time horizon, the relative ranking of the various univariate time series methods may change again.) The relative performance of a particular forecasting method also varies considerably with the origin country being examined. For oneyear-ahead forecasts, the worst forecasts for France are obtained by using autoregression (MAPE) and naive 2 (RMSPE), for FRG by using econometrics (MAPE and RMSPE), for UK by using Gompertz (MAPE and RMSPE), and for USA by using trend curve analysis (MAPE and RMSPE). Econometric forecasts are not ranked particularly high overall in terms of accuracy, but the position achieved relative to the other forecasting methods varies considerably according to origin country. When MAPE is the accuracy criterion (Table 3), econometrics is ranked sec-

MARTIN AND WITT

417

ond for USA, third for France, fifth for UK, and seventh for FRG for one-year-ahead forecasts. When RMSPE is under consideration (Table 4), the only change is that econometrics moves down from second to third position for USA. On moving to two-years-ahead forecasts, the econometric method rankings are the same for both accuracy criteria. Econometrics performs relatively slightly worse for France outward tourism on moving from one-year-ahead to two-years-ahead forecasts, but for the other origins either performs relatively slightly better or retains its previous position. The forecasting performance of the econometric models may also be evaluated in absolute terms in the context of the following classification for MAPEs suggested by Lewis (1982:40) as being applicable to industrial and business data: < 10 % 1O-20 % 20-50% > 50 %

Highly accurate forecasting Good forecasting Reasonable forecasting Inaccurate forecasting.

In terms of the above grading, econometric models do not generate “highly accurate” forecasts for any origin country for either one-yearahead or two-years-ahead forecasts, but do yield “good” forecasts for

Table 4. Forecasting Performance (RMSPE) by Forecasting Method, Origin Country, and Forecasting Horizon Forecasting Horizon 1YeLUd 1

2

Note:

Figures

Origin Country Forecasting Method

FrallWT

FRG

UK

USA

Econometrics

13.61 (3)

13.87 171

27.42 (6)

16.03 13)

Naive 1

11.91 II)

7.57 (1)

14.45 (1)

15.14 (I)

Naive 2

17.85 (7)

13.07 (6)

20.21 (3)

16.75 (4)

Expcmwtial Smoothing

12.68 (2)

9.56 (3)

21.41 14)

15.99 (2)

Gompertz

17.45 (6)

10.84 14)

28.10 17)

20.37 16)

17.16 (5)

11.02 (5)

27.83 (6)

23.74 (7)

Autoregression

16.86 14)

8.30 (2)

18.05 (2)

18.16 (6)

Econometrics

18.19 (4)

24.30 16)

30.22 (4)

13.33 (2)

Naive 1

13.64 (2)

8.54 11)

20.76 (2)

22.28 (3)

Naive 2

27.47 17)

24.87 (7)

38.81 (7)

22.63 (4)

Exponwtial Smoothing

15.46 (3)

13.78 (3)

27.63 (3)

24.58 (6)

Gomperta

22.16 15)

15.61 14)

36.69 (6)

24.34 (6)

Trend Curve Analysis

24.81 (6)

15.63 (5)

37.06 (6)

32.79 (7)

Autorenression

13.54 I11

8.73 12)

19.01 11)

13.87 (1)

in brackets

denote rankings.

418

ECONOMETRIC

FORECASTS OF TOURISM

France, FRG, and USA over both time horizons. The forecasts generated for UK, however, are only “reasonable.” The relative accuracy of the econometric forecasts compared with those generated by the naive 1 model is particularly disturbing. In order to be useful tools, it is generally accepted that forecasting models should be able to predict better than the “no change” model. For example, Theil’s (1966) inequality coefficient U compares the accuracy of forecasts generated by a particular technique with the accuracy of a naive 1 forecast, such that U= 1 if the two techniques perform equally well, U< 1 if the chosen technique performs better than naive 1, and U> 1 if the chosen technique forecasts worse than naive 1. As Makridakis and Hibon (1979:lOO) p oint out: “The U-coefficient is a relative measure, it . . allows comparisons with the naive (X(=X!_., ) or random walk model.” Econometric forecasts only outperform naive 1 forecasts for USA outward tourism flows over the two-years-ahead time horizon. For all one-year-ahead forecasts and for two-years-ahead forecasts from France, FRG, and UK, econometric forecasts are less accurate than naive 1 forecasts, using both measures of forecast performance. Means and Avila (1987) compare one-year-ahead econometric forecasts of US international travel for 1986 generated by the TRAM model with the corresponding forecasts generated by a trend curve model in order to evaluate relative performance. However, Tables 3 and 4 suggest that this comparison is likely to give a more attractive picture of the relative outside sample forecasting ability of the TRAM model than comparison with the standard random walk model. In the present study, for one-year-ahead forecasts of US international travel, econometrics forecasts more accurately than trend curve analysis, but less accurately than naive 1 according to both measures of forecast performance. In fact, the only origin country for which econometrics performs worse than trend curve analysis over a one-year time horizon is FRG.

ANOK The MAPE and RMSPE results presented in Tables 3 and 4 permit evaluation of the relative performance of the various forecasting methods across different origin countries and over different time horizons. In order to test whether there are statistically significant differences in accuracy among the various techniques, an analysis of variance (ANOVA) is carried out. (Recent studies in which ANOVA is used include those by Lawrence et al. 1985, Lusk and Neves 1984, and Price and Sharp 1986.) Thus, it is possible to say at the 5% significance level whether there are statistical differences in forecasting performance among the various forecasting methods. In addition, any significant Zway, 3-way, or 4-way interactions among the factors can be identified. The ANOVA results obtained are exactly the same for both accuracy measures. Forecasting method has seven levels, and statistically significant differences in accuracy exist among the various forecasting methods, so it is clear that some forecasting methods are more accurate than

MARTIN

AND WITT

419

others. The ANOVA results do not indicate, however, where the statistically significant differences lie for the forecasting methods. When the ANOVA results are examined for statistically significant interactions among the factors, it is found that statistically significant 2-way interactions exist. Hence different combinations of two factors have joint impacts on forecasting performance. Significant interactions occur between forecasting method and origin, and forecasting method and horizon, whichever accuracy criterion is under consideration. Thus, for example, a given forecasting method will not necessarily be significantly more accurate than another forecasting method for both one-year-ahead and two-years-ahead forecasts. There are no statistically significant 3-way or 4-way interactions amongst the factors.

If there are more than two levels of a significant factor, it is necessary to perform a further analysis in order to determine which of the factor levels are statistically different from each other. This may be achieved using Scheffe’s multiple comparison test, which is capable of handling unequal cell sizes (see Neter, Wasserman and Kutner 1985). In common with usual practice, the Scheffe test is conducted to show statistically significant differences at the 10% level. As Neter et al. (1985:582) point out: it has been suggested that the confidence coefficient 1 -CY used with the Scheff6 method be below the level ordinarily used, since 1 -a is a lower bound and the actual confidence coefficient will be greater. Confidence coefficients of 90 per cent with the Scheffk method are frequently mentioned. Tables 5 and 6 show the Scheffe test results for the absolute error and squared error performance criteria, respectively. In each Table the accuracy criterion of every factor level under consideration is presented with the smallest mean forecast error on the left and the largest on the right. Values which are not significantly different have a line drawn between them. Examination of the differences among forecasting methods (main effects) in Table 5 shows that the overall MAPE for Nl is the lowest, followed by autoregression, DE, etc. The line drawn between Nl and econometrics demonstrates that the forecasting performance achieved using Nl is not statistically significantly better than that achieved using autoregression, DE, or econometric forecasting methods, but that it is significantly better than the performance obtained by using N2, Gompertz, and TCA. Similarly, the line drawn between autoregression and N2 indicates that although autoregression is significantly better than Gompertz and TCA, it is not significantly better than DE, econometric, or N2 forecasting methods. Overall econometrics is ranked in the middle, and it is neither statistically significantly less accurate than any of the forecasting methods ranked above it, nor significantly more accurate than any of the forecasting methods ranked below it. Examination of the differences among forecasting methods (2-way

420

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Table 5. ScheffG Test Results: DifferrcnrPs Among Forecasting Methods OXWall

MAPE Values and Statistical Signifirance

Nl

Auto

DE

12.41

Nl

12.69

DE I

9.47

ALltO

9.72

Nl 16.18

USA

ECOIl

Auto

Auto I I

ECOII

Gomp

TCA

1 year ahead forecasts

Nl

13.37

DE

12.21

TCA

I

I

21.82

23.17

26.64

Nl

N2

DE

I

I

I

I

19.62

2 years ahead forecasts

Auto 12.11

15.16 15.49

I

I

12.92

13.67

14.72

Nl

ECOll

DE

I

I

15.16

17.88

Nl: Naive 1: NZ: Naive 2; Auto: Autoregression; DE: Double Exponential TCA: Trend Curve Analysis: Econ: Econometrics.

26.93

TCA

18.60

N2

18.11

Gomp

I

16.18

I

14.64

Gomp

I

12.66

N2

12.91

ECOII

I

16.61

I

10.46

N2

14.49

ECOII

I

9.24

DE

14.21

Gomp

I

N2

I

I

Auto

I 10.40

I

12.08

I 11.89

20.07

19.16

6.52

16.23

TCA

I

17.71

DE& TCA

I

Gomp

I I

16.06

Nl

Auto

N2

I

14.79

I 6.02

Econ

I

I

FRG

MAPE

ECOlI

24.63

Gomp

TCA

I

Gomp

I

22.14

Smoothing:

16.97

17.13

N2

TCA

I 23.23

Gomp:

24.08

Gompertz:

interactions) in Table 5 shows that the overall ranking does not hold unchanged for individual origins or forecasting horizons. When methods are considered in conjunction with origin country, there are no statistically significant differences among forecasting methods for outward tourism from France. By contrast, for FRG, autoregression and Nl forecast significantly more accurately than N2; for UK, Nl forecasts significantly more accurately than TCA and Gompertz, and autoregression forecasts significantly more accurately than Gompertz; for USA, econometrics, autoregression, Nl, N2, and DE all generate forecasts which are statistically significantly more accurate than those generated by TCA. When forecasting methods are considered in conjunction with time horizon, Nl generates one-year-ahead forecasts which are significantly more accurate than those generated by Gompertz and TCA. On moving to two-years-ahead forecasts, autoregres-

MARTIN

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421

sion is significantly more accurate than Gompertz, N2, and TCA, and Nl is significantly more accurate than TCA. On examination of the results for RMSPE, it can be seen that the overall ranking of the seven forecasting methods is exactly the same whichever accuracy measure is used, and the only change to statistical significance is that DE does not generate significantly more accurate forecasts than TCA. Examination of subsets of forecasts (2-way interactions) reveals that the ranking does not always correspond exactly between the two accuracy measures. However, Nl always appears in the top three methods for both measures of accuracy, although very few significant differences are indicated between any of the methods when the subsets are considered. Econometric models are less consistently successful as they only feature in the top three methods in two out of the six interaction cases for both MAPE and RMSPE. As often no significant difference between methods is indicated, the conclusions which may be drawn are not absolutely clear cut. However, it appears that three methods should be avoided: TCA, Gompertz, and N2. These three never appear in the top two rankings and where

Table 6. Scheffk Test Results: RMSPE DifferrncesAmong Forecasting Methods

ObWall

RMSPE

Values

and Statistiral

Auto

Nl

Nl

12.63 FRG

IIK

USA

Nl

2 years ahead forecasts

I

I

I

19.39

21.44

23.97

24.22

Econ

Auto

15.60

13.86 Auto

DE

I

I

8.47

11.44

Nl

Auto

DE

I

I

18.48

ECOII

Auto

Nl

I

16.33

Auto

I

I

12.96

N2 I

13.06 N2

I

28.70

29.94

31.65

DE

I

N2

I

16.47

Auto

Nl

DE

I

I 22.77

ECWI

,I 23.41

18.76

32.26

TCA

I

22.16

ECOII

27.98

TCA

Gomp

I

17.67

ECOlI

TCA

Gomp

20.13

22.20

Gomp

I

I

16.10

18.71

I

N2

DE

20.66

I

ECOII

19.49

N2

TCA

I 18.54

26.17

I

19.43

Nl

I

18.41

Gomp

TCA

TCA

I

16.62

24.32

13.00

15.21

Gomp

I

I

17.54

Gomp

I

7.97

14.93

1 ,year ahead forecasts

DE

N2

I

16.74

15.55

ECOII

DE

I

Significance

I 21.45

19.87

22.17

Gomp

N2

I

I

27.66

30.61

Nl: Naive 1: N2: Naive 2; Auto: Autoregression; DE: Double Exponential Smoothing: Gomp: TCA: Trend Curve Analysis: Econ: Econometrics.

TCA 30.80

Gomperta:

ECONOMETRIC

422

FORECASTS

OF TOURISM

significant differences exist, the methods which perform significantly worse than the other methods are always drawn from these three. Of the remaining four methods, significant differences are not indicated, but Nl and autoregressive models usually appear in the top two rankings. Therefore, it seems that these latter two methods may be considered as the most likely methods to produce forecasts with either the minimum MAPE or RMSPE. COMPARISON

WITH

TRAM FORECASTING

PERFORMANCE

In order to see whether the conclusions of this study relating to the forecasting performance of econometric models are supported by the results from other econometric modeling work in the tourism forecasting field, it was decided to examine the forecasts of visits generated by the TRAM econometric model developed by Coopers and Lybrand and published in Means and Avila (1986). Forecasts are given of US outward travel split according to destination country for the years 1986-90. Subsequently (Means and Avila 1987), they analyze the performance of the TRAM model for one-year-ahead forecasts by comparing the forecast with the actual value for 1986. In addition, they evaluate the accuracy of the forecasts generated by the TRAM model relative to 1986 forecasts generated by trend curve analysis (“Growth Approach”) for the European destinations. As Means and Avila (1987: 120) point out: In reviewing an econometric forecasting model such as TRAM, it is a fair question for travel industry analysts to ask how the model performed in predicting travel behavior . it is inescapable that many analysts will want to use TRAM for short-term, one-year forecasts as part of their planning processes.

Table 7 presents the absolute percentage error figures for US travel to each of the European destinations considered in this paper, for both as published by Means and Avila the TRAM and TCA approaches, (1987), together with the MAPE and RMSPE values. In addition, the corresponding percentage error figures are given for the Nl model. It can be seen that the TRAM model forecasts US travel to France, FRG,

Table

7. TRAM

Forecasting Random

Destinat.ion Country FralW? FRG Italy LIK Canada Mexico MAPE ~Europcan destinations) RMSPE (European tkstinations) MAPE la11 destinations) RMSPE WI destinations) Note: ma. denotes not available. Sources: Means and Avila (1986:90-107.

Performance Walk

(Selected

TRAM 28.3 14.1 65.4 0.9 10.2 4.4 27.2 36.3 20.6 30.0

1987: 102-123)

Relative

to Growth

Approach

and

Destinations) Absolute Pwrentage Ehror __ Growth Approach 44.3 36.4 63.5 25.1 ma. n.a. 42.3 44.6 “.a. “.B.

Nl 23.9 14.6 60.1 6.6 12.1 8.8 23.6 28.8 19.2 24.3

MARTIN AND WITT

423

and UK considerably more accurately than the growth approach model, but that the latter model marginally outperforms the former for travel to Italy. Both overall accuracy measures, MAPE and RMSPE, show that the econometric model generates substantially more accurate forecasts than TCA. On comparing the TRAM forecasts with those generated by Nl, however, a very different picture emerges. The random walk model predicts better than TRAM in two out of four cases, and both measures of overall forecasting performance rank Nl above TRAM. In this study, out of the seven forecasting techniques, Nl was ranked top overall, econometrics mid-way and TCA bottom, for both measures of forecasting performance (Tables 5 and 6). When one-year-ahead forecasts of US outward tourism were considered (Tables 3 and 4), the relative ranking of these three forecasting methods was exactly the same: Nl was ranked top (MAPE and RMSPE), econometrics second for MAPE and third for RMSPE, and TCA bottom (MAPE and RMSPE). Hence, it is no surprise to find the same performance ranking for these three forcasting methods when examined within the context of the Means and Avila (1987) study. When the destination country set is extended to include Canada and Mexico (Table 7), so that the Means and Avila destinations correspond exactly to those considered in this study, the overall performance criteria still rank Nl above econometrics, but only slightly in the case of MAPE. The forecasting performance of the econometric model may be evaluated in detail relative to the random walk model by comparing the absolute percentage errors given by Means and Avila (1987) for the TRAM model with the corresponding values generated by the “no change” model. The results are presented in Table 8, together with MAPEs. The MAPE across all foreign destinations for US travelers is 39.2% for Nl, compared with 45.7% for the econometric model. When regional MAPE values are examined, it becomes clear that the econometric model performs badly relative to the random walk model for European destinations, Middle East, and South America. For the Asia/Pacific region, the econometric model is marginally less accurate than the random walk model, and for Carribean and Central America it is marginally more accurate. In terms of absolute percentage errors for individual destinations, econometrics outperforms random walk in 13 cases out of 43 (i.e., 30%): C anada, Mexico, 3 out of 16 European destinations, 1 out of 5 South American destinations, 3 out of 9 destinations in the Asia/Pacific region, and 4 out of 7 destinations in Carribean and Central America. Econometrics forecasts less accurately than random walk for all destinations in Middle East. The fact that the “no change” model outperforms the TRAM model for 70% of the destinations is a poor reflection on the forecasting accuracy of the latter model. The forecasting performance of the TRAM model is far worse when considered relative to Nl than to TCA. Whereas the results presented by Means and Avila (1987), which compare the TRAM model with a growth model, make the TRAM model appear relatively attractive in terms of forecasting accuracy, when compared with a “no change” model the forecasts generated by the TRAM model are relatively inaccurate. Means and Avila justify selection of the growth model for compar-

ECONOMETRIC

424

Table 8. TRAM

Destination

FORECASTS OF TOURISM

Forecasting Performance Relative to Random Walk (All Destinations) Absolute TRAM

Country

Canada Mexico Western Europe United Kingdom France Italy Switzerland Germany (FRG) Austria Denmark Sweden Norway Netherlands BelgiumiLuxembourg Spain

10.2 4.4

12.1 8.8

0.9 28.3 65.4 33.7 14.1 54.7 20.7 2.7 31.0 49.6 13.0 118.3 8.0 179.7 17.6 42.6

5.6 23.9 60.1 36.1 14.6 49.6 11.6 1.2 22.9 39.8 6.2 83.6 17.4 6.7 149.6 9.4 32.9

99.9 83.2 22.7 16.7 66.6

89.3 76.2 13.0 10.0 47.1

22.1 38.6 24.5 585.9 8.4 136.0

10.2 13.1 8.6 637.6 26.7 119.2

36.6 16.6 28.6 24.8 18.4 “Z 108.6 43.3 34.0

32.1 17.1 36.1 33.6 4.6 33.6 0.0 100.0 32.0 32.1

1.9 4.1 4.6 22.1 1.9 7.8 18.6 8.7

1.6 5.9 6.5 23.0 3.0 6.8 17.4 9.0

43.6 %Zla’ Greece Finland MAPE Mid;;&afI=t %ipt Saudi Arabia Kuwait MAPE South America Argentina Brazil Columbia Peru Venezuela MAPE Asia/Pacific Japan Hong Kong Australia New Zealand Korea Singapore Philippines Malaysia India MAPE Carr;$;Uyad Central America Bahamas Jamaica Other British W. Indies Netherlands West Indies French West Indies Other W. Indies/C. America MAPE Sources:

Means and Avila (1986.

Percentage Error Random Walk

1987)

ison purposes on the grounds that the forecasts produced by this model are “conventional” forecasts, and indeed it is not uncommon to generate forecasts using TCA or evaluate forecasting performance in terms of TCA in the tourism field (cf. Tie-Sheng and Li-Cheng 1985; Witt 1989). As O’Reilly (1989) p oints out, “There are many methods used in demand forecasting . . [The] most used quantitative method is trend analysis.” However, the basic standard used for evaluating performance in the forecastingfield in general is the random walk model, and clearly this needs to be adopted more widely in the tourism field. The forecasting performance of the TRAM model may also be eval-

MARTIN

AND WITT

425

uated in absolute terms using the Lewis (1982) classification for MAPEs discussed earlier. The regional MAPEs given in Table 8 show that the econometric model generates “highly accurate” forecasts for Carribean and Central America, “reasonable” forecasts for Asia/Pacific and Western Europe, and “inaccurate” forecasts for Middle East and South America.

CONCLUSIONS Forecasting accuracy has been examined in the context of the application of quantitative forecasting methods to flows of international tourist visits. Several techniques have been used to generate forecasts across a range of origin-destination pairs and differing forecasting horizons, and alternative accepted measures of accuracy have been used to evaluate forecasting performance. The empirical results show that the choice of accuracy criterion does have an effect, but it is not great. There are some differences in rankings and slight differences in statistical significance. In general, the Nl and autoregressive models appear to generate relatively accurate forecasts (although in a few cases no acceptable autoregressive model was obtained), whereas the N2, Gompertz, and TCA techniques produce relatively inaccurate forecasts. DE and econometric forecasts tend to fall in the middle of the accuracy range. The accuracy of econometric forecasting is disappointing. In spite of the likely relative advantage over the other methods resulting from the adoption of an ex post as opposed to ex ante approach, the econometric forecasts are beaten by several others. Support for the empirical results was obtained by examining other econometric forecasts of international tourism demand. Evaluation of the forecasting performance of the TRAM model indicates that Nl tends to generate forecasts which are more accurate than econometric forecasts, with the random walk model outperforming econometrics in 70% of cases. TCA, however, tends to produce relatively inaccurate forecasts compared with econometrics. This consistency of results across the study and the TRAM study was achieved in spite of the use of ex post econometric forecasts in this paper and the TRAM generation of ex ante econometric forecasts. The empirical results obtained are in agreement with Makridakis’ (1986: 18) statement that “Econometric models are not necessarily more accurate than time series (extrapolative) models .” A major advantage of econometric models over time-series models is that the former explicitly take into account the impact on the variable to be forecast of changes in the determining forces, which permits a company to see why changes are taking place through examining the components of the forecast, and to adapt the forecast to new information. Thus the company can link its forecasting with tactical and strategic plans for the future. Hence, a company in the international tourism industry can use an econometric forecasting system to explore the consequences of alternative future policies on tourism demand (“what if’ forecasting), which is not possible with time-series methods. As Makridakis (1986: 17) notes:

426

ECONOMETRIC

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the purpose of econometric models is not purely forecasting. Instead, they attempt to explain economic or business phenomena and increase our understanding of relationships between and among variables. To this direction econometric models provide unique information not available by time series methods.

It should be borne in mind that the results presented in this paper were gained for annual data and should not be generalized to monthly or quarterly observations. Furthermore, the results only apply to oneyear-ahead and two-years-ahead forecasts. Finally, in this paper, the forecast period for France and FRG was 1981-83, for USA was 198184, and for UK was 1981-85. The early 198Os, however, was a period during which immense structural changes took place in the world economy, with the general collapse of world inflation and severe economic recession. In addition, major changes occurred which directly affected tourism, such as lower oil prices and US airline deregulation. Some caution, therefore, needs to be applied in generalizing the results obtained to other time periods, although a later forecast year (1986) was considered in the TRAM study and similar empirical results were obtained. Further research into the relative accuracy of econometric forecasts of international tourism demand is called for. This may include using monthly or quarterly data in model estimation, comparing with different forecasting techniques, generating forecasts over time horizons and generating forecasts for different time greater than two years, periods. 00

Acknowledpmnt- The authors wish to thank COMSHARE ORION forecasting package discussed in this paper.

which

was used to generate

for allowing access to their the time series forecasts

REFERENCES Archer, B. H. 1976 Demand Forecasting in Tourism. Bangor: University of Wales Press. 1980 Forecasting Demand: Quantitative and Intuitive Techniques. International Journal of Tourism Management 1(1):5-12. 1987 Demand Forecasting and Estimation. In Travel, Tourism and Hospitality Research, J. R. B. Ritchie and C. R. Goeldner, eds., pp. 77-85. New York: Wiley. Brown, R. G. 1963 Smoothing, Forecasting and Prediction. New Jersey: Prentice-Hall. Calantone, R. J., C. A. Di Benedetto, and D. Bojanic 1987 A Comprehensive Review of the Tourism Forecasting Literature. Journal of Travel Research 26(2):28-39. Duke, K. E. 1981 Survey of Travel Forecasting Techniques. In Looking Ahead. Eighth Annual Travel Research Seminar, Christchurch, New Zealand, pp. 32-64. San Francisco: PATA Fildes, R. 1985 Quantitative Forecasting-The State of the Art: Econometric Models. Journal of the Operational Research Society 36(7):549-580. Gray, H. P. 1966 The Demand for International Travel by the United States and Canada. International Economic Review 7(1):83-92.

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Institut National de la Statistique et des Etudes Economiques Various issues Annuaire Statistique de la France. Paris: INSEE. Joseph, H., and G. D. Jud 1974 Estimates of Tourism Demand: Latin America. In International Tourism and Latin American Development, W. Krause, G. D. Jud and H. Joseph, eds., pp. 25-42. Austin TX: Universitv of Texas Press. Klein, L. R. 1984 The Importance of the Forecast. Journal of Forecasting 3(l): 1-9. Kliman, M. L. 1981 A Quantitative Analysis of Canadian Overseas Tourism. Transportation Research 15A(6):487-497. Kunst, R., and K. Neusser 1986 A Forecasting Comparison of Some Var Techniques. International Journal of Forecasting 2(4):447-456. Lawrence, M. J., R. H. Edmundson, and M. J. O’Connor 1985 An Examination of the Accuracy of Judgemental Extrapolation of Time Series. International Journal of Forecasting 1(1):25-35. Lewis, C. D. 1982 Industrial and Business Forecasting Methods. London: Butterworths. Loeb, P. 1982 International Travel to the United States: An Econometric Evaluation. Annals of Tourism Research 9(1):7-20. Lusk, E. J., and J. S. Neves 1984 A Comparative ARIMA Analysis of the 111 Series of the Makridakis Competition. Journal of Forecasting 3(3):329-332. Makridakis, S. 1986 The Art and Science of Forecasting: An Assessment and Future Directions. International Journal of Forecasting 2( 1): 15-39. Makridakis, S., and M. Hibon 1979 Accuracy of Forecasting: An Empirical Investigation. Journal of the Royal Statistical Society Series A 142(2):97-125. Martin, C. A., and S. F. Witt 1987 Tourism Demand Forecasting Models: Choice of an Appropriate Variable to Represent Tourists’ Cost of Living. Tourism Management 8(3):233-246. 1988 Substitute Prices in Models of Tourism Demand. Annals of Tourism Research 15(2):255-268. Meade, N., and I. M. D. Smith 1985 ARAMA vs. ARIMA-A Study of the Benefits of a New Approach to Forecasting. Omega 13(6):519-534. Means, G., and R. Avila 1986 Econometric Analysis and Forecasts of U.S. International Travel: Using the New TRAM Model. World Travel Overview 1986/87:90-107. 1987 An Econometric Analysis and Forecast of U.S. Travel and the 1987 TRAM Model Update. World Travel Overview 1987/88:102-123. Ministere du Commerce Exterieur et du Tourisme Various issues L’Economie du Tourisme. Paris: Ministere du Commerce Exterieur et du Tourisme. Neter, J., W. Wasserman, and M. H. Kutner 1985 Applied Linear Statistical Models (2nd ed). Homewood IL: Irwin. O’Reilly, A. M. 1989 Marketing Feasibility Study In Tourism Marketing and Management Handbook, S. F. Witt and L. Moutinho, eds., pp. 253-258. Hemel Hempstead: Prentice-Hall. Price, D. H. R., and-J. A. Sharp 1986 A Comparison of the Performance of Different Univariate Forecasting Methods in a Model of Capacity Acquisition in UK Electricity Supply. International Journal of Forecasting 2(3):333-348. Sheldon, P. J., and T. Var 1985 Tourism Forecasting: A Review of Empirical Research. Journal of Forecasting 4(2):183-195. Statistisches Bundesamt Various issues Fachserie F, Reihe 8, Sonderbeitrag Urlaubs- und Erholungsreisen. Wiesbaden: Statistisches Bundesamt.

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Theil, H. 1966 Applied Economic Forecasting. Amsterdam: North-Holland. Tie-Sheng, W., and G. Li-Cheng 1985 Domestic Tourism Development in China: A Regression Analysis. Journal of Travel Research 24(2):13-16. US Department of Commerce Various issues Survey of Current Business. Washington: US Department of Commerce. Uysal, M., and J. L. Crompton 1984 Determinants of Demand for International Tourist Flows to Turkey. Tourism Management 5(4):288-297. 1985 An Overview of Approaches Used to Forecast Tourism Demand. Journal of Travel Research 23(4):7-15. Van Doorn, J. W. M. ’ ’ 1982 Can Futures Research Contribute to Tourism Policv? Tourism Management 3(3):149-166. Vanhove, N. 1980 Forecasting in Tourism. Tourist Review 35(3):2-7. Witt, S. F. 1980a An Abstract Mode-Abstract (Destination) Node Model of Foreign Holiday Demand. Applied Economics 12(2): 163-180. 1980b An Econometric Comparison of U.K. and German Foreign Holiday Behaviour. Managerial and Decision Economics l(3): 123- 13 1, 1989 Cash Flow Forecasting in the International Tourism Industry. In Advances in Financial Planning and Forecasting, Volume III: International Dimensions, C. E Lee and R. Aggarwal, eds. Greenwich: JAI Press. Witt, S. F., and C. A. Martin 1987 Econometric Models for Forecasting International Tourism Demand. Journal of Travel Research 25(3):23-30. World Tourism Organization 1978 Handbook on Tourism Forecasting Methods. Madrid: WTO. Submitted 2 May 1988 Revised version submitted 7 October Accepted 25 October 1988 Refereed anonymously

1988