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Forecasting h(m)otel guest nights in New Zealand

Christine Lim a,*, Chialin Chang b, Michael McAleer c,d

a Department of Tourism and Hospitality Management, University of Waikato, Private Bag 3105, Hamilton, New Zealandb Department of Applied Economics, National Chung Hsing University, Taiwanc School of Economics and Commerce, University of Western Australia, Australiad Faculty of Economics, Yokohama National University, Japan

1. Introduction

The last two decades have seen a surge in studies on tourism

seasonality, which shows a rising interest in this important aspect

of tourism demand. In their review of past studies on seasonality,

Koenig-Lewis and Bischoff (2005)argue that a substantial part of

the time series literature is related to tourism demand forecasting.

While the findings of these studies are useful, they do not

contribute directly to management and policy-decision issues

related to the hospitality industry. In this paper, we will analyse

tourist accommodation demand and forecast guest nights using

models which should have considerable practical value to the

hotelmotel (henceforth h(m)otel) industry.

The lodging industry, like any other industry, faces challenges

in the process of formulating actions to achieve futuregoals. It tries

to monitor key micro- as well as macro-environmental factors to

assess its strengths and weaknesses, and to discern opportunities

and/or threats. While it is important for hotels and motels to

analyse, for instance customer satisfaction (or lack thereof) in the

product and services of the industry, it is also worthwhile

examining guest demand patterns over time and in the foreseeable

future. Whether the lodging industry is considering short-term

operational planning whereby the environmental conditions are

fixed or long-term strategic planning, where environmental

conditions are uncertain, an analysis of historical demand patternsand demand forecasting is essential for effective planning and

revenue management. This is equally true for the lodging industry

in New Zealand and throughout the world.

The interest shown towards forecasting has come from both

academics and practitioners. Predictions generated by various

forecasting methods are often used as inputs for planning, policy-

making, purchasing decision, inventory control and other business

decision-making activities. Additionally, information on demand

forecasts is essential in the lodging industry for yield management

process and room revenue maximization (Rajopadhye et al., 2001;

Upchurch et al., 2002). It is important to bear in mind that

forecasting is not based on gazing at crystal balls. Any business

forecasting methodusedis often based onfitting a model toa set of

data. Every model has underlying assumptions which are relevant

for forecasting. Temporary or structural changes can occur in the

future due to changes in consumer attitudes, political/economic/

financial events, and technological development, among others.

Such dynamics could cause the existing patterns of travel and

tourist accommodation demand to alter, and forecasting errors are

inevitable.

2. Literature review

Increases in disposable income have seen a rise in recreational

travel demand. The vast majority of domestic and international

tourists who do not stay with their friends or relatives use

International Journal of Hospitality Management 28 (2009) 228235

A R T I C L E I N F O

Keywords:

Lodging industry

Guest night demand forecasting

Time series models

Monthly data

HoltWinters

BoxJenkins

A B S T R A C T

The purpose of this paper is to highlight some time series models which hotel and motel industry

practitioners coulduse to forecast guest nights. Given theirconsiderable practicality, the lodging industry

can easily benefit from using these models as forecasts can be obtained at low cost for effective

management and planning. Monthly observations are used for estimating the model from 1997(1) to

2006(12). The HoltWinters and BoxJenkins ARMA models are able to forecast guest night demand

accurately as 99% of the variations in the guest night forecast are associated with variations in actual

guest nights in 2007.

2008 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: +647 838 4299; fax: +647 838 4331.

E-mail addresses: [email protected](C. Lim), [email protected]

(C. Chang),[email protected](M. McAleer).

Contents lists available atScienceDirect

International Journal of Hospitality Management

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h o s m a n

0278-4319/$ see front matter 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijhm.2008.08.001
mailto:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/02784319http://dx.doi.org/10.1016/j.ijhm.2008.08.001http://dx.doi.org/10.1016/j.ijhm.2008.08.001http://www.sciencedirect.com/science/journal/02784319mailto:[email protected]:[email protected]:[email protected]

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commercial tourist accommodation. With the proliferation of

research in tourism demand using time series models since the

1980s, very few past studies are directly related to the

hospitality industry. The latter is based mainly in the USA and

European destinations and the research undertaken is quite

varied, ranging from estimating visitor hotel expenses, hotel

labour market, and hotel seasonality, to hotel room demand/

occupancy rate forecast.Choi et al. (1999)examined the US hotel

business cycle from 1966 to 1993 and analysed possible turning

points for the industry during this period. In a subsequent paper,

Choi (2003) developed a forecasting tool for the US hotel

industry based on economic (leading, coincident and lagging)

indicators.

Krakover (2000) examined the relationship between labour

turnover and accommodation demand (measured by bed-nights)

in the hotel industry in Israel. Using Danish hotel nights by

regions and tourist nationalities from 1970 to 1996, Sorenson

(1999)proposed an analysis of seasonal unit roots and found that

seasonality is more stochastic than deterministic in nature. In

contrast, Lundtorp (2001) found that the seasonal demand for

Danish hotels was very stable from 1989 to 1998, as measured by

the coefficient of variation and Gini coefficient. In addition to

testing for seasonal unit roots,Gustavsson and Nordstrom (2001)examined the forecast accuracy of various models for the

Swedish lodging (hotels and cottages) industry. Jeffrey and

Barden (1999) used principal component analysis to measure

seasonality of English hotel room occupancy.Koenig and Bischoff

(2004a, b) used a similar technique for the accommodation

sector in Wales.

Choy (1985) and Law (1998) used annual data on tourist

arrivals to forecast the hotel room occupancy rate in Hong Kong.

Since hotel room demand or occupancy rate changes from month

to month, seasonal patterns are ignored in their studies when

annual data are used for forecasting. In a separate paper, the hotel

room rate and occupancy rate in Hong Kong were used as

explanatory variables, among others, by Law (2000) to estimate

and forecast visitor hotel expenses.Rajopadhye et al. (2001)usedthe HoltWinters procedure to forecast room demand for a hotel

which provided the data for the purpose of developing an

intelligent system, presumably for the organization.Cranage and

Andrew (1992)andOlsen and Jose (1982)used time series models

to forecast restaurant sales in the hospitality industry. Of the few

empirical forecasting papers we have identified, Cranage and

Andrew (1992)and Rajopadhye et al. (2001)are the only studies

which have used a substantially large sample of 79 and 58

observations, respectively.

Tourist accommodation can be measured as a flow or a stock.

For instance, the number of hotel and motel rooms available at any

point in time is the stock, whereas the number of room nights

occupied is considered as a flow which changes over a specified

period. The numberof room nights occupied in a hotel or motel permonth as a percentage of room nights available in the enterprise

gives the room occupancy rate during a particular month. Other

important flow concepts include the number of guest arrivals and

guest nights, from which we can estimate the average length of

stay of visitors permonth. For practical reasons, theflow concept is

thepreferred proxyto useas a measure of accommodation demand

in the lodging industry.

The purpose of this paper is to forecast h(m)otel guest night

demand in New Zealand. The rest of the paper is structured as

follows. An overview of major tourist destinations in New Zealand

is given in Section3. In Section4, alternative time series models

used for forecasting are discussed. The unit roottests, methodology

and forecast results are presented in Sections 57, respectively.

Some concluding remarks are given in Section8.

3. Overview of major tourist destinations in New Zealand

In this paper, the data set used on monthly short-term lodging

guest arrivals and guest nights for New Zealand ranges from 1997

to 2007 (Statistics New Zealand, 19972007). In addition to total

guest arrivals, which include domestic and international visitors,

the data are divided into 71 territories, which comprise cities and

districts. Guest arrivals vary from as low as 10 456 in Waimate

district (situated half-way between Christchurch and Queenstown

in the South Island of New Zealand) to as high as about 1.9 million

in Auckland city in 2007.

The five major tourism cities and districts in New Zealand

which receive the most guests are Auckland city, Rotorua district,

Wellington city, Christchurch city and Queenstown-Lakes district.

Their locations in New Zealand are shown in Fig. 1. Auckland,

nicknamed the city of sails, is the largest city and also the

business capital of New Zealand. It is located in the fastest growing

region, which also accounts for more than one-third of the

countrys economy. In Rotorua, tourists experience the natural

wonders of simmering hot springs, erupting thermal geysers and a

wide range of Maori culture. The amazing Waitomo limestone

Glowworm caves are also situated close to the Rotorua district.

Wellington is located at the southern end of the North Island ofNew Zealand. As the capital city of New Zealand, Wellington city is

also home to a wide range of museums, galleries and theatres,

among other attractions.

Christchurch, also known as the garden city, is the largest city

in the South Island. The Southern Alps to the west, and the Banks

Peninsula and Pacific Ocean to the east, where marine activities

such as whale anddolphin watching canbe enjoyed, are among the

many attractions in close proximity to Christchurch. Queenstown

and the Lakes district are renowned for adventure tourism

activities like rafting, skiing, bungy jumping, and its proximity

to stunning landscape in the Fiordland National Parks (AA Travel,

2008). Together, these five tourism regions accounted for about

41%of total guest arrivals in thecountry (see Table 1). Additionally,

total guest arrivals increased by 56% nationally from 1997 to 2007.With the exception of Rotorua district, guest arrivals in the other

four cities and districts grew faster than the country in general.

Fig. 1.Top five cities and districts in New Zealand by guest arrivals, 2007.

C. Lim et al. / International Journal of Hospitality Management 28 (2009) 228235 229

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While the regional seasonal patterns are similar to the national

pattern, what is not known is the concentration of guest arrivals in

these destinations in any 1 year. Among the few papers published

using the Gini coefficient technique to provide evidence on tourist

distributions, we are only aware of one study which examined the

distribution of guest arrivals in the lodging industry in Europe

(Lundtorp, 2001). The Gini coefficient is a very simple and useful

concept borrowed from economics. If the accommodation

enterprise has the same number of guests each month, the Gini

coefficient value is zero. At the other extreme, where all the guests

arrive in one particular month, the Gini coefficient would be equal

to or close to one. Given the monthly variations in guest arrivals,we would expect the Gini coefficient to lie between 0 and 1. A

lower concentration of guests is expected the closer the Gini

coefficient is to 0. When guest arrivals are more spread out

throughout the year, this could alleviate seasonal pressures on the

resources of the enterprise and destination concerned.

As shown in Fig. 2, the three cities and districts in the North

Island of New Zealand have lower Gini coefficients than the two in

the South Island from 2000 to 2007. While Wellington is ranked

fifth in terms of guest arrivals, it has the lowest Gini value and has

only been surpassed by Auckland in 2004. Among the five

destinations, Queenstown-Lakes district is the only one with a

higher Gini value than that of the country. In Lundtorp (2001), the

Gini coefficients for Danish hotels in Copenhagen city and

Copenhagen country from 1989 to 1998 range from 0.12 to 0.14and 0.11 to 0.15, respectively. In comparison to these findings,

Wellington citys Gini values arelower andrange from 0.05 to 0.07.

Information related to short-term tourist accommodation in

the country is collected by Statistics New Zealand as part of their

monthly accommodation survey of commercial lodging providers

with a minimum annual turnover of NZ$30 000. They are classified

under the following five categories: hotels (include resorts), motels

(motor inns, apartments and motels), hosted (private hotels,

guesthouses, bed and breakfast and farm stays), backpackers/hostels, and caravan parks/camping grounds. Fig. 3 shows that

tourist accommodation available from 1997 to 2007 is predomi-

nantly hotels and motels. On average, they accounted for more

than 63% of all accommodation establishments in New Zealand

during this period. Given the larger share of total guest nights from

hotels and motels in the country, we will concentrate on a national

level and forecast the guest night demand patterns of only these

enterprises.

4. Theoretical models

Quantitative techniques used for forecasting consist of regres-

sion models and time series (extrapolative) models (Frechtling,

2001). Econometric models are based on economic theories, andinvolve identifying functional relationships between one depen-

dent variable and one or more related explanatory variables.

Essentially, these models are able to forecast based on regression

analysis. In time series models, the current and past behaviour of a

single variable is extrapolated to predict the future values of the

time series. Extrapolative or univariate time series models have

been standard tools used in tourism and hospitality forecasting for

a number of years because of their low complexity and

computational intensity. In addition to being relatively simple

models, they are especially suited for short-term forecasting as

these models place heavy emphasis on the recent past observa-

tions rather than the distant past.

Examination of the empirical tourism literature on forecasting

methods has found conflicting results. Arguably, statisticallycomplex models do not necessarily perform better, or are no more

accurate than, simpler methods in forecasting (see, for instance,

Burger etal.,2001; Cho, 2003;du PreezandWitt, 2003;Fildes,1985;

Limand McAleer, 2002; Makridakis,1986; Songand Li, 2008; Turner

and Witt, 2001). As hotel and motel guests are both domestic and

international visitors, theuse of regression modelsis notparticularly

appropriate given the complexities associated with the different

demand characteristics and explanatory variables across market

segments. Thus, the use of extrapolative (time series) forecasting

models is more appropriate for this paper. The EViews 5 software

package is used for data analysis and forecasting.

There are numerous extrapolative models of varying degrees

of complexity. They range from basic, intermediate to advanced

methods (Frechtling, 2001). The basic extrapolative methods

Table 1

Summarystatistics on guest arrivalsin NewZealand by major cities/districts,1997

2007

Terr itorial authority S hare (%) 2007 Growth (%) 1997 2007

New Zealand (total) 100 56.2

Auckland city 11 63.9

Christchurch city 10 60.1

Queenstown-Lakes district 8 74.2

Rotorua district 6 25.0Wellington city 6 88.8

Fig. 2.Gini coefficients of the top five regional destinations in New Zealand, 2000

2007.

Fig. 3.Short-term tourist accommodation in New Zealand by type, 19972007.

C. Lim et al. / International Journal of Hospitality Management 28 (2009) 228235230

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include naive and single moving average, while the single, double,

triple exponential smoothing, and autoregression methods belong

to the intermediate category. The BoxJenkins approach is

undoubtedly the most popular advanced extrapolative method

used. More complex forecasting techniques which are rarely used

include, for instance, adaptive filtering, ARCH and GARCH models,

neural network, the State Space approach, and Bayesian forecasting,

some of which are based on engineering principles. For instance, in

the review of 121 studies on tourism/hospitalityforecastingby Song

andLi (2008), onlytwo usedneuralnetwork.Additionally,no studies

usedthe ARCH/GARCH and the State Space approach for forecasting.

The review also highlights the lack of forecasting research in the

hospitality discipline, as only one study used guest nights at the

lodging industry (Gustavsson and Nordstrom, 2001) and the rest

used international tourist arrivals for forecasting.

A time seriestypically consists of three components,namely the

trend-cycle, seasonal and erratic components. As shown inFig. 4,

the total number of hotel and motel guest nights in New Zealand

from 1997 to 2007 trended upwards with seasonality.In this paper,

we will use the HoltWinters triple exponential smoothing and

BoxJenkins models, as these models encompass tourism trend

and seasonality, which are important in forecasting (Box and

Jenkins, 1970; Holt, 1957; Winters, 1960). Furthermore, thesemodels are appropriate for forecasting horizons of 1218 months,

and when a time series with at least 50 observations are available.

The accuracyof a forecastingmethod is determinedby analyzing

the forecast error, which is defined as the actual minus the forecast

(or fitted) value of the variable for time period t, namely:

etAt Ft;

whereetis the forecast error at time t,Atis the actual guest nights

at time t, and Ftis the forecast guest nights at time t.

Although forecasting accuracy is inversely related to the forecast

error, there is not a universally accepted measure of forecasting

accuracy. Forecast optimization typically chooses a model that

minimizes the forecast error. A variety of measures of forecasting

accuracy are available but those which are commonly used includethe root mean squared error (RMSE), the mean absolute (MAE), or

mean absolute percentage error (MAPE) of the forecasts:

RMSEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

n

Xnt1

e2t;

vuut

MAE1n

Xnt1

etj jAt

;

MAPE1n

Xnt1

etj jAt

100:

Unlike past studies which compared the forecast performance

of models based on estimated forecast errors, this paper provides

post-sample forecasts. The latter is of paramount importance for

practical purposes, as the forecast estimates could be used by the

hotelmotel management explicitly for planning and decision-

making. Moreover, goodness of fit canbe computedto show how

well the proposed forecast models have performed when the

actual data become available.

5. Unit root tests

Standard time series analysis rests on the simplifying

assumption that the process which generated the series is

stationary. A stationary process can be defined as one which

has a constant mean, variance and covariance. Using a stationary

model is a sensible strategy as the forecasts converge or revert to

the mean of the series, and it will not generate forecast errors

without limit. Before we estimate time series models for

forecasting, we need to determine whether the underlying

process which generated the series is stationary. The unit root

test is a formal method of testing the stationarity of the observed

time series. A variety of powerful tools is available for testing a

seriesforthe presenceof a unitroot.If the seriesis found tohave aunit root, it is said to be non-stationary. In such a case, an

appropriate data transformation is necessary to obtain a

stationary series.

Monthly guest nights are tested for unit roots using the

PhillipsPerron (PP) test procedure based on the following

regression equation (Phillips and Perron, 1988):

DAta btdAt1 et; (1)

where DAtis the change in the number of guest nights at time t, tis

a deterministic time trend, and etis a disturbance term which is

independent and normally distributed with zero mean and

constant variance. In order to test for unit roots, the hypotheses

of interest areH0 : d 0;H1 : d< 0:

The null hypothesis of a unit root is based on the t-statistic

(which has a non-standard distribution) using simulated critical

values. The PP statistic of4.21 for guest nights is less than the 5%critical value of3.44. Thus, the series is stationary and thecoefficient of the time trend is significant at the 5% level. According

to the PhillipsPerron test, the guest night series does not have a

unit root, so that a data transformation is not necessary for the

series to generate forecasts. The guest night data can also be

described as a trend stationary series.

When modeling seasonal time series within the BoxJenkins

framework, the Hylleberg et al. (1990) (HEGY) procedure is

commonly used to test for the presence of non-seasonal and

seasonal unit roots in a univariate series. The presence of

seasonal unit root implies changing pattern as against a constant

seasonal pattern (Hylleberg, 1992). A test for seasonal unit roots

in quarterly time series by Hylleberg et al. (1990) has been

extended to the monthly case byBeaulieu and Miron (1993)and

Franses and Hobijn (1997). The HEGY test is based on the

following auxiliary regression for monthly observations:

1 L12ytm p1y1;t1p2y2;t1p3y3;t1p4y3;t2 p5y4;t1p6y4;t2p7y5;t1p8y5;t2 p9y6;t1p10y6;t2p11y7;t1p12y7;t2

et; (2)

Fig. 4. Total hotel and motel guest nights in New Zealand, 19972007.


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whereL is the lag operator, defined as Lkyt=ytk (k= 1, 2, . . .).

y1;t 1 L1 L21 L4 L8yt;y2;t 1 L1 L21 L4 L8yt;y3;t 1 L21 L4 L8yt;y4;t 1 L41 L

ffiffiffi3

p L21 L2 L4yt;

y5;t 1 L41 Lffiffiffi

3p

L21 L2 L4yt;y6;t

1

L4

1

L2

L4

1

L

L2

yt;

y7;t 1 L41 L2 L41 L L2yt andetis a normally andindependently distributed error term with zero

mean and constant variance.

Deterministic components which include an intercept, 11

seasonal dummies and a time trend are also included in Eq. (2)

which is estimated by OLS. The null and alternative hypotheses to

be tested are as follows:

H0 : p10; H1 :p1< 0;H0 : p20; H1 :p2< 0;H0 : p3p40; H1 : p3 6 0 and=or p4 6 0;H0 : p5p60; H1 : p5 6 0 and=or p6 6 0;H0 : p7p80; H1 : p7 6 0 and=or p8 6 0;H0 : p9p100; H1 : p9 6 0 and=or p10 6 0;H

0 : p

11p

120; H

1 : p

11 60 and=or p

12 60:

Testing for the significance ofp 0s implies testing for seasonaland non-seasonal unit roots. The HEGY tests involve the use of the

t-test forp1and p2, and theF-tests for {p3,p4}, {p5,p6}, {p7,p8},{p9, p10} and {p11,p12}. We have also conducted theF-test for {p2,

. . .,p12}. The results presentedin Table 2 are compared with the 5%critical values provided byFranses and Hobijn (1997) using 10-

year observations. Diagnostic checking using the Q-statistic and

Lagrange multiplier test indicate there is no serial correlation in

the residuals. The null hypothesis of a non-seasonal unit root

(p1= 0) is rejected while the presence of seasonal unit roots cannot

be rejected. We apply the 12 differencing filter to yt and the

transformed series is denoted by D12yt.

6. Methodology

As the technical details of the HoltWinters and BoxJenkins

methods are well known, this section will concentrate on some

salient features of these models. The HoltWinters exponential

smoothing model has three smoothing parameters. Specifically, the

model computes the average guest nights for the period of interest,

such that themost recent observation receives a greaterweight and

distant observations receive a lower weight in an exponentially

decreasing manner. This smoothing technique can be desirable

because it reduces much of the fluctuations due to the erratic

component in the observed guest night time series. Similarly, a

greater weight is given to the latest trend and seasonality in

determining forecasts for guest nights in New Zealands h(m)otel

industry.

There are two versions of the HoltWinters method, depending

on how the seasonal component is treated. The HoltWinters

Additive method is appropriate if the magnitude of the seasonal

effects in the guest night series do not change. However, if the

amplitude of the seasonal pattern changes over time, then the

HoltWinters multiplicative method would be suitable. Both types

of HoltWinters method are used for forecasting, and the

smoothing estimates (for the level, trend and seasonal parameters)

are generated by EViews in which the sum of squared errors is

minimised. These models which generate an i-period-ahead

forecast (Ft+i) at time t, involve three smoothing equations, one

each for the level, linear trend and seasonal factor:

Forecast : FtLti bti Stj; (3)

Level : LtaAt Stj 1 aLt1 bt1; 0

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The seasonality phenomenon may stem from natural factors

(related to climate, weather, temperature) and/or institutional

factors (related to school vacations, religious festivals, social

customs/practices, other national celebrations and special events).

When we generate alternative ARMA models forthe original series,

seasonal dummy variables are included to account for determi-

nistic seasonal effects. Additionally, the BoxJenkins SARMA

models are estimated for the transformed series, D12yt.

7. Forecasting

In this section, we will evaluate the forecast performance of the

HoltWinters and BoxJenkins approach. Since the BoxJenkins

method is primarily designed for short-termforecasting, a sensible

strategy for the BoxJenkins procedure is to estimate different

combinations of AR(1), AR(2), MA(1) and MA(2) models with a

constant and eleven seasonal dummies. According to Frechtling

(2001), it is seldom useful to proceed beyond these models into

higher order ones (p. 130). Similarly, different combinations of AR,

MA, SAR and SMA models with values forp, q, Pand/or Q 2, and aconstant are estimated for the 12 differenced series, D12yt.

Only models with all significant parameter estimates at the 5%

level andwith no serial correlation areselected. We have identified

twoand elevensuch ARMA andSARMA models, respectively. Using

selectioncriteriasuch as the Akaike information criterion(AIC)and

Schwarz Bayesian criterion (SBC), the ARMA and SARMA models

with the smallest AIC and SBC values are selected to generate

forecasts. Accordingly, ARMA(2,1) and SARMA(2,0,1)(1,1,0)12 are

the optimal models for forecasting h(m)otel guest night demand in

New Zealand.

As suggested in Frechtling (2001), we will retain the most

recent data available. The HoltWinters and BoxJenkins models

are used to generate forecasts, and the latter is tested against our

retained data. In this way, we can evaluate how well these

models perform, before we generate forecasts beyond the known

values of the series (see the figure below). Specifically, our

estimation sample is monthly guest nights from January 1997 to

December 2006, from which we develop the optimal forecast

models. These models are used to generate 1-month-ahead

forecast for 12 periods. The forecast estimates (also known as ex

post forecasts) can then be compared with the monthly guest

night data available in 2007. This will help to determine which

model produces the best forecasts. These models are subse-

quently used to compute future values of guest nights (that is, ex

ante forecasts).

The smoothing estimates for the level of the series are 0.25 and

0.21 for HoltWinters additive and multiplicative method,

respectively. The zero values estimated for the trend and seasonal

components show that they are fixed or not changing. These

smoothing estimates are subsequently used in the HoltWinters

model to generate forecasts. The guest night forecast from the

HoltWinters and BoxJenkins models are given in Fig. 5. Itis clear

that the HoltWinters and ARMA methods outperform the SARMA

model in tracking the guest night series in 2007. The correlation

coefficient is also computed as a goodness-of-fit measure to show

how well the models forecast guest nights. Table 3shows that the

correlation coefficients of the BoxJenkins and HoltWinters

models range from 0.25 to 0.99. Undoubtedly, the fitted ARMA

and HoltWinters models forecast guest night demand in hotels

and motels very well, as 99% of the variations in the guest night

forecasts are associated with variations in actual guest nights in

2007.These modelsare subsequentlyusedto generateex anteforecasts

(for which actual data arenot yetavailable)for 18 months from2008

to 2009. Theresultsare presented in Table 4 and Fig.6. In 2007,hotel

and motels in New Zealand experienced on average a negative

growth of 1.0% in monthly guest night demand. The HoltWinters

additive and multiplicative methods predict negative growth of

1.752.1% between 2008 and 2009. In comparison with these

methods, the forecast estimates generated by the BoxJenkins

ARMA model is quite pessimistic. Guest night demand forecast for

the 18-period is substantially lower than 2007.

Fig. 5.Estimated ex post guest night forecasts for New Zealand, 2007.

Table 3

Correlation coefficients between actual and predicted guest nights in New Zealand

using BoxJenkins and HoltWinters models, 2007

Model RMSE Correlation coefficient

HoltWinters additive 57 999 0.991

HoltWinters multiplicative 45 963 0.991

ARMA(2,1) 83 755 0.990

SARMA(2,0,1)(1,1,0)12 61 178 0.245

Table 4

Estimated ex ante guest night forecasts for New Zealand, 2008 and 2009

Forecast horizon ARMA HWA HWM

2008M01 2 182 497 2 217 443 2 312 218

2008M02 1 269 705 2 125 478 2 200 621

2008M03 1 325 343 2 146 563 2 219 948

2008M04 1 052 537 1 898 895 1 918 279

2008M05 722 002 1 490 660 1 414 683

2008M06 795 923 1 417 737 1 317 410

2008M07 1 107 549 1 707 524 1 674 551

2008M08 920 682 1 632 380 1 583 679

2008M09 1 022 108 1 717 422 1 685 558

2008M10 1 110 693 1 852 285 1 858 331

2008M11 1 164 342 1 965 650 1 991 069

2008M12 1 123 169 1 939 484 1 953 235

2009M01 1 456 574 2 274 977 2 385 358

2009M02 1 226 175 2 183 012 2 270 048

2009M03 1 282 494 2 204 097 2 289 801

2009M04 1 010 358 1 956 429 1 978 482

2009M05 680 484 1 548 194 1 458 965

2009M06 755 054 1 475 271 1 358 540

Note: ARMA, HWA and HWM denote the autoregressive-moving average, Holt

Winters additive and HoltWinters multiplicative methods, respectively.


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8. Conclusion

It is found that there are some variations in the growth and

distribution of lodging guest arrivals in selected destinations in

New Zealand. However, we do not expect the small regions to

have significant influence on the overall national patterns of

guest nights in the h(m)otel sector. The purpose of this paper

was to highlight some time series models which the hotel and

motel industry practitioners could confidently use to forecast

guest nights at the national level. Given their considerable

practical value and usefulness, the industry can benefit from

using these models since forecasts can be obtained at low cost

for effective planning. It is essential that a sufficiently large

sample is used for estimation, and the fundamental nature of the

data used is not violated so that the approach to forecasting isrobust. The latter includes unit root testing for stationarity and

diagnostic checking of models before selecting optimal models

for forecasting.

While recognizing that a myriad of models is available, we

support the view that some form of forecasting undertaken by the

hospitality industry is better than none at all. Depending on the

amount of resources the industry is prepared to invest in obtaining

forecasts as inputs for their business planning and operations, this

will determine the type of technique to use. The findings of this

paper show thatrelatively simple models, such as the HoltWinters

method, can forecast as well as the ARMA model and better in

comparison with the statistically sophisticated BoxJenkins SARMA

model. Furthermore, this method is available in many econometric

software packages such as EViews, which is menu driven and userfriendly. With adequate ex post forecasts achieved, and at low cost,

their practical value and usefulness are considerable. The h(m)otel

industry can, therefore, benefit significantly from time series

forecasts, and save in lower inventory costs.

Theissue as to whether it pays to combine forecasts of a variable

hasbeendebated fromthe 1970ssince theBates andGranger(1969)

path-breaking article was published. In addition to comparing the

forecast performance of competing models, Granger and Newbold

(1986) have argued that an alternative forecast, which is simply the

averageof individual forecasts, might be more successful. According

toPalm and Zellner (1992), a simple average of individual forecasts

has worked well in practice, whereby equal weights are assigned to

individual forecasts. The potential usefulness of combined forecasts

will be considered in future research.

Acknowledgements

The authors are grateful to the editor and two anonymous

reviewers for helpful comments and suggestions. The second

authorwishes to acknowledge thefinancialsupport of theNational

Science Council (NSC 97-2410-H-005-004-), Taiwan. The third

author is grateful for the financial support of the Australian

Research Council.

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