Forecasting

ARTICLE IN PRESS

Tourism Management 25 (2004) 209–218

Forecasting tourism demand: a cubic polynomial approach
Fong-Lin Chu*
Graduate Institute of National Development, National Taiwan University, No. 1, Roosevelt Road, Sec. 4, Taipei, Taiwan
Received 27 November 2002; accepted 16 April 2003

Abstract
This paper examines the accuracy of a forecasting model in predicting internationaltourism arrivals, as represented by the
number of worldwide visitors to Singapore. The cubic polynomial model is employed to forecast the volume of tourist arrivals from
January 1989 to July 1990. The results are then compared with studies of the accuracy of forecasts by earlier work. The results
demonstrate that the cubic polynomial method generates a slightly higher value of mean absolutepercentage errors than that of sine
wave nonlinear regression and seasonal–nonseasonal ARIMA. However, the cubic polynomial model has the advantage of
generating forecasts with lower cost because of its intrinsic linearity. Finally, the diagnostic tool is applied to identify those
predictive errors that manifest unusual features, and which result in deterioration of the mean absolute percentageerror as our
forecasting horizon expands.
r 2003 Elsevier Ltd. All rights reserved.
Keywords: Forecasting; Cubic polynomial function; Mean absolute percentage errors; Mean-shift outlier model; Predictive error; Singapore;
Studentized residuals; Tourism demand

1. Introduction
International tourism has grown rapidly over the
last two decades and is now second only to oil in
world trade.However, the rate of growth has
varied immensely from year to year, and while
most countries have enjoyed steady increase in their
tourist arrivals, some experienced declines in numbers at
certain times. Planning under these circumstances is
exceptionally difficult and important. But in an attempt
to plan successfully, accurate forecasts of tourism
demand is required. This point has been notedby several authors in the tourism field. For example,
Wandner and Van Erden (1980, p. 381) point out
that:
Since governments and private industry must plan
for expected tourism demand and provide
tourism investment goods and infrastructure, the
availability of accurate estimates of international
tourism demand has important economic consequences.
*Tel.: +886-2-23630231x3587; fax:+886-2-87324146.
E-mail address: flchu@ccms.ntu.edu.tw (F.-L. Chu).
0261-5177/03/$ - see front matter r 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0261-5177(03)00086-4

Archer (1987, p. 77) emphasizes the particular
necessity for accuracy in tourism demand forecasting:
In the tourism industryythe need to forecast
accurately is especially acute because of the perishable nature of the product.Unfilled airline seats and
unused hotel rooms cannot be stockpiled and
demand must be anticipated and even manipulated.
Benefits derived from an accurate forecasting system
is imaginable. In the case of forecasts of demand turning
out too high, firms in related industries will suffer; there
might be, for instance, empty seats on airplanes and
coaches, empty rooms in hotels, unoccupiedapartments,
unused rental cars, and so on. It is likely that in general
capital investment will be excessive, the labor force will
be too huge and excess stocks will be held of goods
normally sold directly to or used by tourists. If, on the
other hand, the case turned out to be that forecasts of
demand are too low, then firms will lose opportunities;
for example, there may be inadequate hotelaccommodation or too few flights to cater for all those wishing to
visit a certain location at a given time. Even if supply
can be expanded to a limited extent at short notice, this
is likely to impose additional costs on firms as, say, less

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F.-L. Chu / Tourism Management 25 (2004) 209–218

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efficient aircraft are used, and excessive overtime is
worked.
The end of the...