Computers, Materials & Continua DOI:10.32604/cmc.2022.022309 | |

Article |

A New Hybrid SARFIMA-ANN Model for Tourism Forecasting

1Artificial Intelligence & Data Analytics Research Lab (AIDA), CCIS Prince Sultan University, Riyadh, 11586, Saudi Arabia

2Department of Statistics, University of Gujrat, Gujrat, 50700, Pakistan

3Department of Statistics, University of Sialkot, Sialkot, 51310, Pakistan

*Corresponding Author: Mirza Naveed Shahzad. Email: nvd.shzd@uog.edu.pk

Received: 03 August 2021; Accepted: 29 October 2021

Abstract: Many countries developed and increased greenery in their country sights to attract international tourists. This planning is now significantly contributing to their economy. The next task is to facilitate the tourists by sufficient arrangements and providing a green and clean environment; it is only possible if an upcoming number of tourists’ arrivals are accurately predicted. But accurate prediction is not easy as empirical evidence shows that the tourists’ arrival data often contains linear, nonlinear, and seasonal patterns. The traditional model, like the seasonal autoregressive fractional integrated moving average (SARFIMA), handles seasonal trends with seasonality. In contrast, the artificial neural network (ANN) model deals better with nonlinear time series. To get a better forecasting result, this study combines the merits of the SARFIMA and the ANN models and the purpose of the hybrid SARFIMA-ANN model. Then, we have used the proposed model to predict the tourists’ arrival in New Zealand, Australia, and London. Empirical results showed that the proposed hybrid model outperforms in predicting tourists’ arrival compared to the traditional SARFIMA and ANN models. Moreover, these results can be generalized to predict tourists’ arrival in any country or region with a complicated data pattern.

Keywords: SARFIMA; hybrid model; tourists’ arrival forecasting; ANN

The rapid development in the tourism industry in the last 30 years has contributed to many countries’ economies. According to the World Travel & Tourism Council (WTTC), 2019, tremendous evolution was observed in the tourism industry. It has created 313 million jobs and created prosperity in industries related to tourism and has increased taxations. As a result, the tourism industry had generated 10.3% of the global GDP. Consequently, every country is paying much attention to growing tourists’ arrival in their territory. Therefore, tourism policy makers and business practitioners are interested in knowing an accurate forecast of tourist volume for properly distributing resources and formulating pricing strategies [1].

One well-known approach to model tourists’ arrival data is to use time series models. For this purpose, models based on the Box-Jenkins methodology have been extensively used in the past several decades. For example, the autoregressive integrated moving average (ARIMA) and its sub-models are well-recognized to predict future observations based on linearly correlated past observation and a white noise error term. However, these models work efficiently only for short memory time series processes [2]. On the other hand, most time-series data, including financial data, stock-exchange data, and numbers of tourists’ arrivals, have long memory characteristics. For such types of time series data, Granger [3] introduced the autoregressive fractional integrated moving average (ARFIMA) model that speculates the ARIMA by allowing non-integer values of the differencing parameter

The ARFIMA model has been applied in several studies for accurate forecasting. For example, Doornik et al. [5] forecasted US and UK inflation rates using the ARFIMA model and showed its superiority over the ARIMA model. Chu [6] has found better forecasting about tourists’ demand in Hong Kong, Japan, and Korea by ARFIMA model than ARIMA. Moreover, Cheung [7] used the ARFIMA model for predicting the foreign exchange rates. Along with the ARFIMA model, Prass et al. [8] also applied the seasonal autoregressive fractional integrated moving average (SARFIMA) model to predict the mean monthly water level Paraguay River in Brazil. The SARFIMA model has also been used by Mostafaei et al. [9] to predict Iran's oil supply. In recent years, Peng et al. [10] developed the new hybrid random forest-LSTM model to forecast tourist arrival data and justified by the Beijing city and Jiuzhaigou valley data that this hybrid approach outperforms. Waciko et al. [11] used the Thief-MLP hybrid approach to forecast short-term tourists’ arrival to Bali-Indonesia. Wu et al. [12] forecasted daily tourist arrival to Macau SAR, China with a hybrid SARIMS–LSTM approach and obtained the good fitted results.

It is important to note that all Box-Jenkins models require the linearity of the process under study (see, e.g., [13]). This means that future observations should have a linear relationship with present and past observations. Therefore, ARFIMA and SARFIMA models become inappropriate when time series are generated from nonlinear processes. Nonlinear models such as the Artificial Neural network (ANN) have been used in several studies to overcome this problem. For instance, Sarvareddy et al. [14] studied the characteristics of ANN and showed its forecasting power over traditional time series models. Zhang et al. [15] studied ANN forecasting for seasonal and trend time series and showed that the ANN has nonlinear architecture and performs well for linear time series. In several studies, ANN has been constantly compared with the traditional Box-Jenkins model and long memory models, and its better performance is justified. Prybutok et al. [16] observed that the ANN analysis performs better for time series datasets, specifically in the presence of nonlinearity.

Note that there is no definitive proper measure to check whether the process generated from time series is linear or nonlinear. Therefore, it would be difficult to decide in advance which model should be used. Furthermore, there is no standard model that is appropriate for both linear and nonlinear time series data. Therefore, by combining the characteristics of two or more models, the accuracy can be increased. Different hybrid models have been developed following this idea, particularly by combining linear autoregressive models and ANN models. The beauty of these types of hybrid models is that they can capture the characteristics of both linearity and non-linearity in the time series [17]. This idea was first used by Zhang [18] to introduce a hybrid methodology that combines both ARIMA and ANN models. Following [18], a hybrid of ARIMA models and support vector machines (SVMs) were used by Pai et al. [19] to forecast stock prices. Chen et al. [20] examined the forecasting accuracy of the hybrid of seasonal ARIMA (SARIMA) and SVM models for Taiwan's machinery industry production. Chaâbane [21] found a hybrid of ARFIMA and ANN model more efficient over individual ARFIMA and ANN to predict electricity price.

Moreover, Chaâbane [22] found a better performance of hybrid ARFIMA–least-squares SVM than the competing models while predicting electricity spot prices. In general, practitioners rely on two methods to forecast tourist volume. One is time series analysis methods [23] and the other is artificial intelligence methods [24–26]. However, many recent studies have proved that the combination of the aforementioned methods leads to better forecasts [27–29].

In the present study, our main interest is to introduce a new hybrid model for better and accurate prediction using the complicated time series data, the new hybrid model is proposed by hybridizing the SARFIMA and ANN model using the Zhang [18] approach. The second goal is to evaluate the predictability of the developed model on the different natured tourists’ arrival datasets, for this, the datasets of the three countries were retrieved and better results have been obtained. Finally, the performance of the suggested model is verified using out-of-sample data as real-time analysis, and the results predicted by the model matched with the real tourists’ arrival values.

The rest of the paper is organized as follows. An overview of ARFIMA, SARFIMA, and ANN models is given in Sections 2, 3, and 4, respectively. The proposed hybrid SARFIMA-ANN model is presented in Section 5. Section 6 reports on the proposed hybrid model's empirical results using three real datasets on tourists’ arrival and discussion. The concluding remarks are given in Section 7.

When there is a long memory presence in time series data, the frequently used model is the ARFIMA model, introduced by Granger et al. [30] and its properties were further investigated by Baillie [31]. Let us assume that

where

where

3 SARFIMA

There are several situations in which time-series data have a long memory and exhibit periodic patterns. The appropriate model for such time-series data is the SARFIMA

Proposition 1: Let

When t ∈ (−1, 0), then the process

Proposition 2: Let

where

where

Proposition 3: Assume that

i. The process

ii. The stationary process

iii. The stationary process

Based on Katayama's previous work [34], model estimation using SARFIMA requires a few steps. Firstly, identifying the long memory process and finding fractional difference parameter

4 Artificial Neural Network Based Forecasting

When the restriction of linearity on time series data is relaxed, enormous nonlinear models have been developed for obtaining better forecasts. An artificial neural network (ANN) is one of them. The critical characteristic of ANN over other nonlinear models is its ability to deal with a large class of functions. Moreover, ANN does not require any prior assumption for the estimation process. Instead, its architecture is entirely determined from the characteristic of data. For more details on ANN, we refer the interested readers to [35].

The ANN architecture consists of an input layer, an output layer, and multiple hidden layers depending upon the complexity of data. Information passes through each layer in terms of neurons. For forecasting time series data (

where

The ANN model in (3) can be termed as univariate nonlinear autoregressive (NAR) model, that is:

Here

Since there is no standard mechanism to determine the appropriate ANN architecture for the given data, multiple experiments can be conducted to choose suitable values for p and

5 Hybrid Methodology and the Proposed Hybrid Method: SARFIMA-ANN

The tourists’ arrival time series data may consist of many components such as linearity, nonlinearity, seasonality, heteroscedasticity, or a non-normal error. One standard approach for forecasting such time-series data dealing with all components does not exist. One may think SARFIMA is a better option for this case. However, SARFIMA cannot deal with complex nonlinear structures. The second choice might be the ANN, which deals well with nonlinear structure but may also provide unsatisfactory results when modeling the linear data [37]. In other words, both SARFIMA and ANN models are successful only in their domains. Zhang [18] introduced hybrid models that can model both linear and nonlinear structures of time series data to overcome this problem.

Following Zhang [18], we propose a hybrid of the SARFIMA and ANN model in this study. In the proposed model, time-series data is composed as a function of linear and nonlinear components. To be more precise,

The different methods can estimate the linear and nonlinear parts of (5) to develop the model. The defined methodology used in this work has three steps. In the first step, the linear portion of the time series data is modeled by SARFIMA, considering it follows a long memory process. From the fitted SARFIMA model, the forecasted values

where g(.) is a nonlinear regression function determined by the ANN model. This provides us the prediction of the nonlinear part

The pictorial representation of our proposed hybrid methodology is given in Fig. 1. In addition, the algorithm of hybrid SARFIMA-ANN is presented in Fig. 1.

6 Application and Empirical Results

To check the performance of the proposed hybrid SARFIMA-ANN model on forecasting tourists’ arrival, we consider the three real data sets. As, over the past three decades, tourism has become one of the world's most flourishing industries. International tourists’ arrival has conventionally been used as a benchmark to assess any country's security condition and economic development. It significantly impacts GDP, employment rate, import and export, and many public and private sectors. This significant impact attracts the researcher to study the flow of tourists’ arrival in a particular country. The number of tourists’ arrivals can be considered a time series process due to the consistent change over time and therefore, the prediction model may be applied. Tourists’ arrival data get more attention in several studies (see, [38–40]). In this study, the following three tourists’ arrival datasets are considered to implement and justify the proposed hybrid model's competency over the other models.

Dataset 1. This dataset is related to the tourism industry, growing gradually in New Zealand due to its amazing natural attraction sites. To forecast tourists’ arrival in this country, monthly data from January 2000 to September 2018 is retrieved from https://www.stats.govt.nz, a sample of 225 observations. The plot of this dataset in Fig. 2 depicts that the considered data is stationary in the mean but has seasonal variation. The autocorrelation function and partial autocorrelation function showed the presence of seasonality at

Dataset 2. The second dataset contains the monthly number of tourists’ arrival in Australia from January 2000 to August 2018, giving 224 observations, which are retrieved from https://www.abs.gov.au. The data series is regarded as nonlinear and non-Gaussian and suitable to evaluate for analysis. This time-series data has been plotted in Fig. 3, showing seasonality at

Dataset 3. The proposed model is also applied to the number of tourists’ arrival in London, UK. The quarterly data set has 66 observations, corresponding to 2002Q1–2018Q2, taken from https://www.data.london.gov.uk and plotted in Fig. 4. There exist seasonal fluctuations at

These three datasets are used in the present study to demonstrate the effectiveness of the proposed hybrid method. Note that these tourists’ arrival datasets have seasonal fluctuations due to seasonal changes and this situation requires explaining such fluctuations by some suitable seasonal models. The summary of the datasets is given in Tab. 1. The considered datasets are far from normality as indicated by skewness and kurtosis values and further confirmed by the Jarque-Bera test. Furthermore, Augmented Dickey-Fuller, Philips–Perron, and Kwiatkowski, Phillips, Schmidt, and Shin tests indicate that dataset 1 is stationary whereas the other two datasets are non-stationary. To make the datasets suitable for analysis, datasets are made stationary by taking first differences. Then, long memory parameter d and Hurst parameter H are estimated to ensure that the considered data sets follow long memory processes. For tourists’ arrival datasets of New Zealand, Australia, and London, the estimated values for

In order to apply and explain the performance of SARFIMA, ANN, and hybrid SARFIMA-ANN models, the datasets are partitioned into the training and testing part. To be more precise, New Zealand tourists’ arrival data from January 2000 to December 2015 (85.71%) is considered to train models and the set from January 2016 to August 2018 (14.29%) is considered for model testing. Similarly, Australian tourists’ arrival data from January 2000 to December 2015 (87.71%) is used for model training, and the rest from January 2016 to August 2018 (14.29%) is considered for model testing. Similarly, in London tourists’ arrival data, set from first quarter 2002 to fourth quarter of 2013 (72.73%) is considered a training set and from first quarter 2014 to the second quarter, 2018 (27.27%) is considered a testing set. This partition of datasets is also sketched in Fig. 5.

6.1 SARFIMA Model for Tourists’ Arrival Datasets

The fitting of SARFIMA

6.2 Artificial Neural Network Model

To obtain the most accurate ANN model, numerous ANN models were established for the considered datasets using two hidden layers with varying 2 to 30 nodes in the first hidden layer, and 2 to 7 nodes in the second hidden layer. By varying the number of nodes in the first and second hidden layers, 145 models are developed, whereas each model is trained 50 times. Due to the space limitation, the detailed results are not presented here. However, from these models, the best models are selected based on minimum mean squared error (MSE) and root mean squared error (RMSE). Consequently, we obtain ANN

The hybrid algorithm mainly consisted of two steps as discussed earlier. In the first step, a SARFIMA model is fitted to analyze the linear part of the data and in the second step, the residuals from the SARFIMA model are analyzed. Linearity in the residuals is checked using the BDS test as suggested by Broock et al. [41]. In order to perform the BDS test, the following steps are being followed.

i. Select embedded dimensions

ii. Calculate the correlation coefficient that

Here

iii. Compute BDS test statistic that is defined as

iv. It is a two-tail test. The statement under the null hypothesis will reject when the BDS test statistic is greater than the critical value.

In Tab. 3, the results of the BDS test on residuals from selected models SARFIMA models such as SARFIMA (3, 0, 1)(10, 0, 7

The numerical results of the BDS test, as in Tab. 3, favour rejecting the null hypothesis about the time series linearity at a 5% level of significance. It demonstrates that the errors (residuals) from the best selected SARFIMA models have nonlinear patterns. This indicates that only the linear model (SARFIMA model) is not adequate to model the data well. Therefore, implementation of nonlinear models also requires, such as ANN, to capture the nonlinearity pattern.

We consider the best selected SARFIMA and ANN models, and build the hybrid SARFIMA and ANN models for New Zealand, Australia, and London tourists’ arrival data. Recall Zhang [18] that one can use separate suboptimal models to develop the hybrid method. Following their suggestion, the optimal SARFIMA model is used to model the linear part of the data and the nonlinear patterns fitted by the finalized ANN model. Then the improved prediction is obtained by combining the output of the best fitted SARFIMA and ANN model in the hybrid SARFIMA-ANN model. The performance indicators, that is, MSE and RMSE of the proposed hybrid SARFIMA-ANN and the individuals SARFIMA and ANN models, are presented in Tab. 4. The comparison of the results clearly shows that the proposed hybrid SARFIMA-ANN outperforms than the competing models. Furthermore, the out-of-sample performance of the hybrid and individual models is shown in Fig. 6. We see that the forecasting obtained by the hybrid SARFIMA-ANN model in each dataset is closer to actual than the competing models.

Tourism is a rapidly growing industry in most countries and it is demanding more accurate modeling and forecasting of tourists’ arrival data for many purposeful decisions. This, in turn, has grabbed increasing attention to more accurate and advanced forecasting methods. Therefore, the main interest of the study was to establish a possibility for the improvement in the forecast accuracy of tourist arrival using a hybrid modeling approach. Recently, the extension of the SARIMA, which is called the SARFIMA model, has become popular for the linear time series data with long memory processes and periodic patterns. More recently, the ANNs have shown much flexibility in modeling the nonlinear data. Therefore, ANN and SARFIMA can only achieve accurate results in their premises, and generally, none of them is the best model for every forecasting situation. Thus, in this study, a hybrid SARFIMA-ANN approach is established and applied to forecast tourists’ arrival in Australia, New Zealand, and London. This approach is outperformed and produced promising results in the actual situation and produces positive results compared to the two competitors, SARFIMA and ANN. Our results have implications both for theory and application. Theoretically, we developed a hybrid SARFIMA-ANN model. In terms of application, the results of hybrid SARFIMA-ANN provide confidence for policymakers in the search volumes of tourists’ arrival. Consequently, the proposed hybrid SARFIMA-ANN model and the investigation of this study make a good step in improving the forecast accuracy in tourists’ arrival.

Acknowledgement: This research is supported by Artificial Intelligence & Data Analytics Lab (AIDA) CCIS Prince Sultan University, Riyadh 11586 Saudi Arabia. The authors also would like to acknowledge the support of Prince Sultan University for paying the Article Processing Charges (APC) of this publication.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no interest in reporting regarding the present study.

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Appendix

A hybrid algorithm based on SARFIMA and Neural network

Hypothesis:

Input: Time series dataset

# Fitting SARIMA model

Set:

for j in (1:

if j

R (j) =

else

end if

end for

# Fitting ANN model

Set:

for k in (1:

End for

Output:

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