Modelling and Forecasting Tourism Demand for Sri Lanka

Modelling and Forecasting Tourism Demand for Sri Lanka G.K.A. Dias#1, C. Hettiarachchi#2, D.D. Karunaratne#3, W.H. Kodituwakku#4, D.M. Wijesundara#5 #

University of Colombo School of Computing Reid Avenue, Colombo 7, Sri Lanka 1 [email protected] , [email protected], [email protected], [email protected], [email protected] Abstract- Accurate forecasts of tourist arrivals are of critical importance to the tourism industry. It would help to ensure the availability of required infrastructure and services when demand materializes. This study aims at forecasting tourist arrivals to Sri Lanka. To achieve this, monthly tourist arrival data from January, 2010 to August, 2014 was analyzed by building a number of models to ascertain the best model to forecast tourist arrivals. The main reason for selecting this time period was the boost of tourist arrival seen after the end of the civil war in 2009, resulting political stability and the recognition of Sri Lanka as a safe tourism destination. The results show that Holt Winters Multiplicative Seasonal Model delivers the most accurate predictions. This was tested against the SARIMA, Holt Winters Additive Seasonal Model and NARX neural network. In this study, neural network were identified as an alternative approach for forecasting. But the forecasting accuracy of the neural networks was relatively low due to the limitations of the available data set. But when such limitations are removed the use of neural network approach for forecasting may yield better results. Keywords- tourism demand, time series forecasting, Lanka, neural networks

I.

INTRODUCTION

Tourism plays a vital role in Sri Lanka’s economy by contributing to foreign exchange earnings, employment generation, government revenue and initiation of business opportunities. Tourism industry in Sri Lanka has grown with uneven swings over the years. The advantage of Sri Lanka as a tourism destination is mainly based on two reasons. Firstly it is an authentic tourism destination. Secondly it is a compact island of 65,610 square kilometers where a tourist can travel the length and breadth of the country within a comparatively short period. During the 30 years up to 2009, Sri Lankan tourism has had many obstacles mainly due to the unsecure political situation that prevailed. This situation was also aggravated by the Tsunami disaster in 2004. The global economic crisis occurred in 2008 has also had a major impact on the industry [1]. At present-day, all these holdups are resolved. The steady and safe political state of affairs awakened in the country after the civil

war was ended in 2009 has increased the attraction towards Sri Lanka as a safe tourist destination. According to 2011 estimates, the total contribution to Gross domestic product (GDP) from the travel and tourism sector was 8.4 % while that same sector directly and indirectly supported approximately 590,000 jobs. In 2012, Sri Lanka's tourism marked a significant achievement by welcoming more than one million tourists within the year [2]. Forecasting is very important in many types of organizations since predictions of future events are essential for the decisionmaking process. Any information concerning the future volumes and patterns of tourism flows is important for hoteliers, tour operators and other industries concerned with tourism or transportation, in order to plan their investments and marketing strategies. Also government institutes need accurate forecasts of demand for tourism to plan and provide for the required tourism infrastructures, such as accommodation site planning and transportation development, among other needs. The tourist arrivals variable is still the most widely held measure of tourism demand over the past few years. Specifically, this variable was measured by total tourist arrivals from an origin to a destination. The research problem addressed in this study is how to identify models that can be recommended for accurately forecasting of the total tourism demand and the number of tourist arrivals from main origin countries to Sri Lanka. To address this problem, monthly tourist arrival data from January, 2010 to August, 2014 was analyzed by building several models (i.e. Holt Winters Additive and Multiplicative Seasonal Models, SARIMA and NARX network) to ascertain the best model to forecast tourist arrivals. The scope of this research is the post war era in Sri Lanka and relies heavily on secondary data for the construction of the model and for estimation. The forecasts of international tourists‟ arrivals to Sri Lanka would be in respect of six origin countries of Sri Lankan tourism industry. This paper is organized as follows. The section which immediately follows is a review of the relevant literature and the succeeding section describes the research methodology. Then, the results and analysis are presented and the final section presents the conclusions.

II.

LITERATURE REVIEW

Total number of persons who travel or wish to travel, to use tourist facilities and serviced at places away from their places of world and residence is called tourism demand [3]. Basically, the literature on modeling and forecasting tourism demand is huge with various types of empirical analyses. Some of the researchers apply cross-sectional data, but the majority of studies used pure time series analytical models where the objective is forecasting of tourism demand. Tourism forecasting researchers have to rely predominantly on secondary data, collected by governments or other agencies. Because of the nature of these data, tourism demand is usually measured by the numbers of tourists arriving at particular destinations from particular departure points [4]. Tourism demand is characterized by abrupt directional changes in trends, seasonality and the impacts of events such as wars and natural disasters, all of which make the forecasting process more challenging. The cycle of tourism demand from a particular country might lag behind the economic cycle in that country, so an economic downturn can be indicative of a fall in tourists from that country a few periods later. On seasonality, there is some evidence to show that seasonal patterns exhibit mean reverting behavior which means that despite sometimes straying from established patterns, they tend to return to these established patterns in the long term [5]. A. Tourism Demand Forecasting The existing literature suggests that there are mainly two categories of forecasting methods; firstly qualitative methods which refer to a variety of non-scientific techniques including insights used to predict future events and secondly quantitative methods which qualify past information about a phenomenon by applying mathematical rules which take advantage of the underlying patterns and relationships in the data. Time-series methods and the econometric methods are both used to evaluate the tourism demand and forecasting. In addition, other methods, such as the artificial neural network (ANN), the rough set method, the fuzzy time series (Fuzzy), and genetic algorithms (GAs), among others, are also used. The time-series method and the econometric method are among the most utilized methods while the other methods, such as ANN, Fuzzy and GAs, are being used less frequently [6]. B. Time Series Approaches A time series model explains a variable with regard to its own past and a random disturbance term. Particular attention is paid to exploring the historic trends and patterns (such as seasonality) of the time series involved, and to predict the future of this series based on the trends and patterns identified in the model [6]. Time-series models have been widely used for tourism demand forecasting in the past four decades with the dominance of the Holt Winters Methods and integrated autoregressive moving-average models (ARIMA) [7]. Depending on the frequency of the time series, either simple ARIMA or seasonal ARIMA (i.e., SARIMA) models could be

used with the latter gaining an increasing popularity over the last few years, as seasonality is such a dominant feature of the tourism industry and the decision makers are very much interested in those seasonal variations. Since time series models only require historical observations of a variable, it is less costly in data collection and model estimation [8]. Goh and Law (2002) introduced a multivariate SARIMA (i.e. MARIMA) model which includes an intervention function to capture the potential spill-over effects of the “parallel” demand series on a particular tourism demand series. Their study showed that the multivariate SARIMA model significantly improved the forecasting performance of the simple SARIMA as well as other univariate time series models [9]. C. Artificial Neural Networks In addition to the time series, artificial intelligence (AI) techniques have emerged in the tourism forecasting literature. In ANN Models we can include determinant variables. A study to forecast Japanese tourist arrivals in Hong Kong has presented a new approach [7] that uses a supervised feed-forward neural network model. The input layer of the neural network contains six nodes: Service Price, Average Hotel Rate, Foreign Exchange Rate, Population, Marketing Expenses, and Gross Domestic Expenditure. The single node in the output layer of the neural network represents the Japanese demand for travel to Hong Kong. Estimated Japanese arrivals were compared with actual published Japanese arrivals. Their experimental results showed that using the neural network model to forecast Japanese arrivals outperforms multiple regressions, naive, moving average, and exponent smoothing [10]. Qualitative methods are not used as a main method for forecasting method because they are based on expert opinion and judgment. Therefore Qualitative methods have to integrate with quantitative method. Most of the researchers use qualitative method as a base and add weighted qualitative variable to the base equation. Qualitative methods help to improve accuracy and reduce gap between actual and forecasted results. Some researchers have attempted to combine the forecasts generated from different models in order to improve the forecasting accuracy. General forecasting literature suggests that forecast combination can improve forecasting accuracy. To overcome the limitations of quantitative forecasting approaches and further improve forecast accuracy researchers have also tried to integrate the quantitative forecasting methods with qualitative alternatives The application integrative approach is reported in a study which introduced an integrative approach that combines statistical techniques with expert opinions in a quasi-Delphi process to gather key industry input to the forecasting process. This approach was employed to forecast South Australia’s international and domestic tourism markets [6]. D. Evaluation of Forecasting Accuracy A forecast may not be 100% accurate all the time; actual demand may deviate from the forecasts. The objective of forecasting is that such deviation would be as slight as possible.

Most researchers who are forecasting tourism demand use the size of the forecasting errors [11] to examine the performance of their tourism demand forecasting models. The majority of tourism demand forecasting studies in the past have used the Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE) or Root Mean Square Percentage Error (RMSPE) and Theil‘s U as means to examine the forecasting performance of their tourism demand forecasting models [4]. There is no singlet winning method in tourist demand forecasting. The comparative accuracy of approaches depends on factors like how far ahead one is in forecasting and whether it is for monthly, quarterly or annual demand. The performance of the forecasting models varies according to the data frequencies used in the model estimation, the destination-origin country/region pairs under consideration and the length of the forecasting horizons concerned. III. METHODOLOGY This study adopts a quantitative research approach which can be defined as the systematic empirical investigation of phenomena via statistical, mathematical or numerical data or computational techniques such as neural networks. The study is entirely based on secondary data on monthly international tourist arrivals to Sri Lanka and other economic indicators extracted from annual statistical reports of Sri Lanka Tourism Development Authority (SLTDA) and The International Monetary Fund (IMF). Time series trend analysis and seasonal factor analyses are the main procedures of data analysis. Also this approach was adopted since the research develops and employs statistical and neural network models and is supposed to do quantitative forecasting. Scientific research is a systematic and objective process. It involves gathering of a multitude of information for analysis so that the researcher can come to a reasonable conclusion. The main goal of this study is to support information needs of all stakeholders of Sri Lankan tourism industry by providing forecasts about tourist arrivals. To achieve this goal in this research project, following process was followed up.

Problem Identification

Literature Review

Research Design

Data Collection Analysis

Select Forecasting Methods

Implementation

Evaluating Forecasting Performance

Select Best Models and Forecast Tourism Demand

Discussion and Conclusions

Fig. 1. Research process

After the literature review, and once data have been collected for the time series analysis and forecast, the next step would be the selection of forecasting models. Various statistical and graphical techniques would be used for the selection of the models which have the potential to produce the best forecasts. After reviewing literature on tourism demand forecasting, it was decided to select time series and artificial neural networks based models for the forecasting endurance to ensure the selection addresses the major categories of forecasting methods. After selection of a model, the next step is its specification. The process of specifying a forecasting model involves selection of the variables to be included, selecting the form of the equation of relationship, and estimation of the values of the parameters in that equation. Historical tourist arrival data will be used to build and fit the selected forecasting models (both statistical models and neural networks). In the data analysis phase for neural networks and econometric models - in addition to the monthly numbers of tourist arrivals - exogenous variables would also be selected based on the findings of the literature review. In this study, the sample comprises the aggregate number of tourists who arrive in Sri Lanka every month. In their study Kurukulasuriya and Lelwala emphasized that a linear trend pattern is existing while the obvious seasonal pattern is recognized in tourist arrivals for Sri Lanka. They further revealed the absence of cyclical and significant irregular variations. Their study confirmed that the linear trend component and seasonal fluctuations are significant components of international tourist arrivals to Sri Lanka for the period from July 2009 to June 2013 [1]. Therefore it was decided to select forecasting models which can address both trend and seasonality. The variables that were used in this research are the numbers of international tourist arrivals to Sri Lanka during 2010-2014, monthly exchange rates between Sri Lankan Rupees (LKR) and the currencies of the origin countries during that period, Annual per capita Gross Domestic Product (GDP) and Google Trends web search indexes under Travel Category (i.e. search term “Sri Lanka”). For the evaluation purposes of this study is proposed to predict tourist arrivals from six countries to Sri Lanka. Of the six, five were selected on the basis of the higher percentage share of total tourist arrivals during 2009-13 periods. Those countries are India (16.4% of overseas arrivals in 2013), United Kingdom (10.8%), Germany (6.7%), Maldives (6.2%) and France (5.0%). In addition, it was noted that arrivals from China (4.3%) are showing an accelerating growth rate during past few years. Due to this reason, China was included in our list of six tourist originating countries, even though China is not among the top six in the 2009 -13 period. Together, arrivals from these six markets accounted for 49.41% of all international tourist arrivals in 2013. The selected forecasting models for this research (based on the critical review done on the literature and the data analysis)

are explained in below. Although researchers still not unanimous in deciding which model is the best to be used in tourism forecasting a model that produces the least error is most commonly identified. It should also be noted at this point, that the comparative forecasting results are not meant to be conclusive in term of model choice, but rather help to illustrate the potential of origin country based forecasting. A. Holt-Winters Seasonal Method Holt-Winters Seasonal Method is used when the data shows trend and seasonality. This method has two versions, additive and multiplicative, the use of which depends on the characteristics of the particular time series. The latter will be considered first. The Holt-Winters seasonal method comprises the forecast equation and three smoothing equations - one for the level 𝑙𝑡 one for trend 𝑏𝑡 , and one for the seasonal component denoted by 𝑠𝑡 , with smoothing parameters α, β∗ and γ. We use m to denote the period of the seasonality, i.e., the number of seasons in a year (e.g. quarterly data 𝑚 = 4, and for monthly data 𝑚 = 12) [12]. There are two variations to this method that differ in the nature of the seasonal component. The additive method is preferred when the seasonal variations are roughly constant through the series, while the multiplicative method is preferred when the seasonal variations are changing proportional to the level of the series [12]. B. Holt-Winters Additive Seasonal Model The method produces exponentially smoothed values for the level of the forecast, the trend of the forecast, and the seasonal adjustment to the forecast. This seasonal additive method adds the seasonality factor to the trended forecast, producing the Holt-Winters’ additive forecast [12]. In this model, we assume that the time series is represented by the model; 𝑦𝑡 = 𝑏1 +𝑏2 𝑡 + 𝑆𝑡 +∈𝑡

(1)

Where; 𝑏1 is the base signal also called the permanent component 𝑏2 is a linear trend component 𝑆𝑡 is an additive seasonal factor ∈𝑡 is the random error component Let the length of the season be L periods. The seasonal factors are defined so that they sum to the length of the season, i.e; ∑ 𝑆𝑡 = 0

(2)

1≤𝑡≤𝐿

With the additive method, the seasonal component is expressed in absolute terms in the scale of the observed series, and in the level equation the series is seasonally adjusted by

subtracting the seasonal component. Within each year the seasonal component will add up to approximately zero [12].

C. Holt-Winters Multiplicative Seasonal Model This is similar to the Holt-Winters’ additive method. HoltWinters’ Multiplicative method also calculates exponentially smoothed values for level, trend, and seasonal adjustment to the forecast. In this model, we assume that the time series is represented by the model; 𝑦𝑡 = (𝑏1 + 𝑏2 𝑡)𝑆𝑡 +∈𝑡

(3)

Where; 𝑏1 is the base signal also called the permanent component 𝑏2 is a linear trend component 𝑆𝑡 is a multiplicative seasonal factor ∈𝑡 is the random error component The length of the season is indicated as L periods. The seasonal factors are defined so that they sum to the length of the season, i.e. ∑ 𝑆𝑡 = 𝐿

(4)

1≤𝑡≤𝐿

This seasonal multiplicative method multiplies the trended forecast by the seasonality, producing the Holt-Winters’ multiplicative forecasts [13]. D. SARIMA Model Seasonal Autoregressive Integrated Moving Average (SARIMA) model is an extension of the ordinary ARIMA model to allow for seasonality in the data. With a seasonal time series, it can be made stationary by seasonal differencing which is defined as a difference between a value and a value with lag that is a multiple of S [9]. The Seasonal ARIMA model incorporates both non-seasonal and seasonal factors in a multiplicative model with the form of ARIMA (p,d,q) (P,D,Q) S, Where: p, d, q are the parameters in non-seasonal ARIMA model as mentioned above. P is the number of seasonal Autoregressive order, D is the number of seasonal differencing, Q is the number of seasonal Moving Average order, and S is the time span of repeating seasonal pattern. SARIMA (1, 1, 1) (1, 1, 1) 12 model yields the following equation: 𝐹𝑡 = 𝜙1 𝑋𝑡−1 + Φ12 𝑋1−12 − 𝜙1 Φ12 𝑋1−13 + 𝜉𝑡 − 𝜃1 𝜁𝑡−1 − Θ12 𝜀𝑡−12 − 𝜃1 Θ12 𝜁𝑡−13 (5)

With φi and θi the non-seasonal parameters that are estimates, Φi and Θi the seasonal parameters, and ξt an uncorrelated random shock. E. NARX Network “Nonlinear Autoregressive models with eXogenous input” (NARX) model is a dynamical neural architecture commonly used for input-output modeling of nonlinear dynamical systems. The original architecture of the NARX network can be easily and efficiently applied to prediction of time series using embedding theory to reconstruct the input of NARX network [14]. A state space representation of recurrent NARX neural networks can be expressed as; 𝑧𝑘 (𝑘 + 1) = {𝜑(𝑢(𝑘), 𝑧𝑖 (𝑘)), 𝑧𝑖 (𝑘), 𝑖 = 1, 𝑖 = 2,3, … 𝑁}

(6)

where the output 𝑦(𝑘) = 𝑧𝑖 (𝑘)and 𝑧𝑖 , 𝑖 = 1,2, … 𝑁 are state variables of recurrent neural network [14]. The NARX model can be implemented by using a feedforward neural network to approximate the function. A diagram of such network is shown below, where a two-layer feedforward network is used for the approximation. This implementation also allows for a vector ARX model, where the input and output can be multidimensional.

Fig. 2. NARX Network

In addition to use of time and number of tourist arrivals for the NARX network it was decided to use search query volume data (i.e. travel category in Google Trends search volume index from each origin country), exchange rates and GDP per capita (the gross domestic product divided by mid-year population) of the respective countries as exogenous inputs for this study. The variables that are affecting the numbers of tourist arrivals were identified based on literature. Those variable selections were done according to the correlation coefficient of the variables. Pearson’s correlation analysis has been used to analyze the correlations within the variables. Google Trends, Exchange Rate and Time respectively indicated 0.5340, 0.6279 and 0.8359 values in Pearson’s correlation for Total Tourist Arrivals. This shows positive relationships which are greater than 0.5. F. Evaluation of Forecasting Accuracy

Using above selected methods, the total tourist arrivals and arrivals from the selected six originating countries were forecasted and the performance of those forecasts were evaluated. Arrival data from January 2010 to February 2014 were used for the calculations and arrival data for March 2014 to August 2014 were used for the evaluation purposes. Evaluation of forecasts and the selection of the best model were done using the Accuracy Measure models. Selected accuracy measure models are Root mean square error (RMSE), Mean percentage error (MPE), Mean absolute percentage error (MAPE) and Theil’s U. The model which yields the minimum and the most proximate value to the zero in an accuracy model would be considered as the most suitable forecasting model for the respective originating country. IV. RESULTS AND ANALYSIS It is important to evaluate forecast accuracy using genuine forecasts. That means even though a model fits well with the historical data that alone would not be sufficient. The accuracy of forecasts should be determined by considering how well a model performs on new data that were not used when fitting the model. When choosing models, it is common to use a portion of the available data for fitting, and use the rest of the data for testing the model, as was done in the above mentioned models. Then the testing data can be used to measure how well the model is likely to forecast on new data. In this study, the sample contains the aggregate number of tourists who arrive in Sri Lanka every month. Occurrence of civil war and Tsunami disaster in Sri Lanka affected the number of tourists but this number returned to normal in 2010. Therefore, the data were obtained between January 2010 and August 2014, covering a total of 56 months. The data for this study were obtained from the annual statistical reports issued by Sri Lanka Tourism Development Authority (SLTDA). Apart from those, exogenous inputs for NARX network (i.e. Google Trends (search engine query volume data), exchange rate and GDP per capita) were obtained from the World Bank’s publications. The accuracy of forecasts can be determined by considering how well a model performs on new data that were not used when fitting the model. When choosing models, it is common to use a portion of the available data for fitting, and use the rest of the data for testing the model, as was done in the above mentioned models. Then the testing data can be used to measure how well the model is likely to forecast on new data [2]. The previous data covering 50 months from January 2010 to February 2014 was used to establish the tourism demand forecasting model. Consequently, we compared the forecasted number and the actual number of tourists who visited Sri Lanka during the following 6 months from March 2014 to August 2014 in order to understand the accuracy of the model. As mentioned earlier selected accuracy measures were; Root Mean Square Error (RMSE), Mean Percentage Error (MPE), Mean Absolute Percentage Error (MAPE) and Theil’s

U. Accuracy of results forecasted by the selected models are included in succeeding table for total tourist arrivals and tourist arrivals from six origin countries. By considering the respective minimum error values of forecast models, the most suitable models are highlighted and indicated in table 1. TABLE I COMPARISON OF THE FORECASTING ACCURACY OF THE MODELS RMSE

MPE

MAPE

Theil’ sU

Additive

7128.971

-4.0979

5.2146

0.0593

Multiplicativ e

4410.590

0.9690

2.6611

0.0367

SARIMA (011)(010)

8274.625

-4.5205

6.7786

0.0688

NARX

18917.55 0

2.3889

14.481 1

0.1573

Additive

1394.018

-4.5952

5.1797

0.0718

Multiplicativ e

1212.396

-3.6254

5.4012

0.0624

2148.063

5.8203

9.8958

0.1106

3354.574

10.777 4

Additive

1571.181

-3.0917

11.914 5 10.792 3

Multiplicativ e

1592.299

-0.9545

8.6429

0.1285

1830.744

-8.0256

14.641 1

0.1477

4751.348

26.802 3

44.087 0

0.3834

997.957

2.5637

10.839 7

0.1179

1087.222

8.7689

9.2739

0.1285

SARIMA

1275.430

13.603 5

20.015 1

0.1507

NARX

1175.278

6.1783

16.313 9

0.1389

1336.643

19.063 6

19.063 6

0.2055

964.112

-3.9041

13.403 9

0.1482

26.568 7

0.2809

24.288 9

0.2762

India

Total Arrivals

Model Holt Winter s

Holt Winter s

SARIMA(110)(100)

France

Maldives

Germany

United Kingdom

NARX Holt Winter s SARIMA NARX Holt Winter s

Holt Winter s

Additive Multiplicativ e

Additive Multiplicativ e

SARIMA

1827.058

NARX

1796.885

Holt Winter s

Additive Multiplicativ e

SARIMA

China

NARX Holt Winter s

Additive Multiplicativ e

26.568 7 16.850 3

0.1727 0.1268

722.557

-6.5953

15.034 4

0.1027

1455.236

28.926 5

28.926 5

0.2067

638.084

-1.8085

1794.505

5.1844

2663.652

5.5130

2922.232

SARIMA

3143.825

NARX

4721.369

15.160 5 19.869 6 43.068 6

10.296 5 21.141 4 14.863 9 16.092 5 19.869 6 43.068 6

As mentioned earlier when selecting best forecast model, priority has been given to the accuracy measures of those models. All four accuracy models were considered according to the country and if more than two accuracy models indicate minimum error in particular forecast model; that forecast model was selected as the best. If two forecast models got two minimum errors in two accuracy models (Ex: United Kingdom), average changed ratio between actual results and forecasts results have been considered. In such instances, the forecast model which gives the lowest changed ratio (see Appendix) between results has been taken as the best model. For forecasts of total tourist arrivals, Holt Winters Multiplicative Seasonal Model provides best results. All accuracy measure models also indicated minimum errors in the Multiplicative model. Three accuracy measure models indicated minimum values for Multiplicative model in Indian tourist arrival forecasts. In United Kingdom best model selection, two forecast models got equal chances in accuracy measures. Thus consideration of results changed ratios was required. According to those ratios the Additive model gave a 10.8% difference and the Multiplicative model gave an 8.6% difference. Holt Winters Multiplicative Seasonal Model has the minimum deviation and it was selected as the best forecast model for UK. For German tourist arrivals forecast the Additive model gave the best results and showed minimum error in three accuracy models. Holt Winters Multiplicative Seasonal Model, SARIMA and Holt Winters Additive Seasonal Model were selected respectively for Maldives, France and China. All those models have been selected based on accuracy measure models as all four models indicated minimum error in each particular forecast model.

0.0907 0.2549

Fig. 3. Total tourist arrivals from March, 2014 to August, 2014) - actual and forecasted values

0.2507 0.2750 0.2959 0.4444

Figure 1 shows the graphical illustration of results regarding total tourist arrivals. After the best model selection procedure, the results are presented in separate graphs for the respective models. Based on the assessment of forecasting accuracy of the various models, it is possible to conclude that the Holt Winters Multiplicative Seasonal Model is superior to the other

forecasting models (i.e. Holt Winters Additive Seasonal Model, SARIMA and NARX network). Both - the actual arrivals line and Holt Winters Multiplicative Seasonal Model line - follow same up and down directions while overlapping many times. The forecasting process and performance evaluation confirms that the forecasting models that took into account the seasonal nature of tourist arrivals in Sri Lanka outperformed the other models over all forecasting horizons. Therefore, from a methodological point of view, one has to recognize that international tourist arrivals are seasonal and this has to be accounted for in the modelling process at first. Secondly, Holt Winters Multiplicative Seasonal model proved to deliver the most accurate predictions of arrivals over the Holt-Winters Additive Seasonal Model, SARIMA and NARX neural network. By applying Holt Winters Multiplicative Seasonal Model in forecasting tourist arrivals in Sri Lanka could support government and the private sector in preparation of their respective policies, strategies and decision making process to have products and services available to fully absorb and cater to the future tourist arrivals. However, one of the drawbacks of using time series techniques in forecasting arrivals is that it does not identify the underlying causes for the changes in arrivals. V. CONCLUSION Tourism sector is on an upward trend after the end of the civil war in Sri Lanka. The analysis of data confirms that a linear trend and seasonal fluctuations are significant components of international tourist arrivals to Sri Lanka during the period under review; i.e. from January 2010 to August 2014. Tourist arrivals have significant peaks in the months of February, June, July and August while months of September and October were identified as mini peaks. The highest numbers of arrivals were recorded in July. Therefore, the seasonal component is a significant issue in managing tourist related businesses and thus this information is explicitly valuable for those who are engaged in tourist related industries. This study used different time series and a neural network method to model and forecast tourist arrivals in Sri Lanka from six originating countries (i.e. India, United Kingdom, France, Maldives, Germany and China). The tested models were; Holt Winters Additive and Multiplicative Seasonal Models, SARIMA and NARX network. Holt Winters Multiplicative Seasonal Model provides fairly accurate forecasts of tourist arrivals in Sri Lanka, particularly for the short run. As such, it remains a popular approach to forecast tourist arrivals. However, this method does not make provision for assessing the influence of external events and therefore its policy application is limited. The main limitation of this research was the inability to use a larger post sample data period. Medium and long term forecasting accuracy could not be tested and the findings of the

research are limited to the short-term. This was due to the use of only the post-war tourist arrival data (after 2009) for forecasting purposes. In the current Sri Lankan context we find that NARX network is usually the least accurate forecasting technique due to these limitations in the availability of data. This constraint will gradually be removed as the arrival series becomes longer. Although the selected statistical forecasting models are good examples of modern methodology, NARX network approach can be more successful with a larger data set. Holt Winters Multiplicative Seasonal Model forecasts provide fairly accurate forecasts of tourist arrivals in Sri Lanka, especially over the short run. As such, it remains a popular approach to forecast tourist arrivals. However, this method does not make provision for assessing the influence of external events and therefore its policy application is limited. The tourism industry is unsympathetically affected by a wide range of factors such as serious social conflicts, wars and economic crises to name but a few. However, the degree of impact varies and is not easily quantifiable. Therefore it is important for researchers to develop forecasting methods that can accommodate unexpected events and predicting the potential impacts of these events through scenario analysis. Findings from this study are the direct measures from quantitative models, and the literature review suggests that further refinement by expert opinion using a qualitative method may be the better way to increase the overall level of accuracy. Artificial Neural Networks (ANNs) are an established and powerful computational approach to data analysis and they are comparatively more close to the abilities of the human brain. Importantly, ANNs have the ability to learn from the existing and adapt to new information. This makes ANNs more powerful than traditional statistical forecasting approaches [15]. Although data availability will remain an important constraint, there would be some potential for improving the accuracy of ANNs approaches in the future. The findings of this study can be used by authorities of tourism in Sri Lanka to produce a better tourism plan for the development of the industry. However, it should be kept in mind that this type of processes are subject to change with time and current time series model may not be appropriate for a longer time span. Therefore, it is recommended to have a periodic monitoring of the data series as well as forecasts. Forecasts should be updated whenever new information becomes available. ACKNOWLEDGMENT We would like express our sincere gratitude to Dr. C. Tilakeratne (The Department of Statistics of the University of Colombo). She contributed with precious time and given us invaluable suggestions and guidance to make this research a reality. We would also like to express our thanks to Sri Lanka

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