Forecasting Vietnamese tourists’ accommodation demand using grey forecasting and ARIMA models

The development of the tourist accommodation sector significantly contributes to the overall growth of tourism. The need for accurate predicting the demand for tourist accommodation of international and domestic tourists is a key goal for future good preparation and appropriate strategy. The objective of this study is to show some Grey forecasting models involving GM (1, 1), Verhulst, DGM (1,1), and ARIMA models consist of ARIMA (0, 1, 1) for the projection of the future number of domestic and international visitors serviced by tourist accommodation establishments in Lam Dong province. The author of this study applies four essential criteria Mean absolute percentage error (MAPE), Mean absolute deviation (MAD), Mean square error (MSE), Root mean square error (RMSE) to compare the various forecasting models outcomes and to examine which suitable forecasting models can improve the capability to project the number of future international and domestic tourists served by tourist accommodations in Lam Dong province. The monthly statistics of number tourists serviced of tourist accommodation and total revenue from tourist accommodation service in Lam Dong province covering in the period from January 2012 to October 2018 are obtained from the official website of general statistics office of Lam Dong province and statistical yearbook of Lam Dong in order to guarantee the accuracy of forecasting procedure. The key findings of this study are that ARIMA (1, 1, 1) (1, 1, 1) model can effectively predict the number of domestic tourists with more accurate outcomes with a minimum predicted errors. Besides that, the number of international visitors serviced by tourist accommodation can be obtained more accurately by using the ARIMA (1, 1, 1) (1, 1, 1) model. In the case of total revenue from tourist accommodation service in Lam Dong province, ARIMA (0, 1, 1) (0, 1, 1), GM (1, 1), DGM (1, 1) models have better performance than the Verhulst model. The forecasting results also showed the number of international and domestic tourists serviced by tourist accommodation in Lam Dong is growth slightly. Therefore, Lam Dong Authority must make good preparation and appropriate strategies to response exactly at any changes and supply for tourist accommodation markets.


Introduction
* Tourist accommodation is a fundamental element of the tourism product to the tourists. It has close correlation with the development of tourism industry. The classification (for example: luxury, low-budget hotel), scope and nature of accommodation are the key factors to determine the value and volume of tourism that is probable at any tourist attraction places. Industry needs in tourist accommodation sectors have become more shortterm concentrated, and aimed to change quickly with continuous changing characteristic of market need. In recent years, the number of both domestic and international tourists visit Lam Dong, especially Da Lat, strongly increased. This has led to the diversity and the dramatic growth in number and improvement of the quality of local hotel-related business and services such as motels, hotels, homestay (Fig. 1). Tourist accommodation sector in Lam Dong province from 2009 -2017 has developed substantially.
In 2009, there were 735 accommodation establishments with the capacity of 9,970 rooms. These numbers tend to go up significantly in 2017 in which 1,155 accommodation establishments and 17,726 rooms. According to the Vietnam National General Statistics Office, the amount of spending of on tourist accommodation service has been increased slightly in group of domestic visitors starting from 6.93 USD in 2005 to 13.63 USD in 2017 (Fig. 2). The international visitors tend to go up more significantly in the period of 12 years beginning from 19.2 USD to 30.3 USD. In general, the tendency of tourists' consumption on lodging is higher over time which creates a potential environment for the growth of overall tourism. However, this sector is facing some challenges: lack of timely management concentration, limited number of professional human resources in hospitality industry, ineffective control in price which causes the conflict of interest between hotelrelated business owners and visitors. According to the Ministry of Culture, Sports and Tourism of Vietnam, the quality inspection procedure of tourist accommodation sector mostly focuses on the inspection of three to five-star rating hotels. Besides that, in the period 2010 -2015, the three to five-star hotels after the inspection or ratings procedure have been negligent in sanitation and quality management. Tourists' spending on tourist accommodation

Research objectives
Tourism depends on many different sectors and industries, one of which is the hotel and tourist accommodation. There have been fluctuations in the number of international and domestic visitors as well as purpose of visit, length of stay and type of tourist accommodation. The uncertain number of tourists affects the hotel industry, a key player in tourism. There is a lack of strategic and control planning for hotel development in each particular region by the Vietnamese governments and there are no accurate figures for developers' reference. Therefore, many hotel projects have carried out based on developers' assumptions about the future demand of rooms or in other words, the number of tourists accommodated by lodging services in the cities. The hotel or tourist accommodation industry in some specific areas has not been able to reliably forecast the number of tourists requiring accommodation. For the objective of competition with other regions and attracting more potential visitors, it is obvious that visitor accommodation in Lam Dong province needs an accuracy vision for future tourists' demand of hotel. In order to response to the uncertainty of accommodation needs for the tourists arriving in a specific area, there is needed a model that can project the future accommodation demands by the tourists. These projections will make it possible for the players in the hotel industry to react in appropriate time to the anticipated changes in tourist accommodation demand over time and also to maximize returns on investments.
The need for accurate tourist accommodation projection is a vital component in hotel or visitor accommodation industry planning and management strategies. Thus, this study presents the model of ARIMA, GM (1, 1), Verhulst, DGM (1, 1) to test which models can handle the forecast accuracy of this situation.

Tourist accommodation
Holiday accommodation or lodging is a basic foundation of tourism industry since it is an essential and fundamental component which tourism supplies to satisfy customers' requirements of location where they can relax and revive during their trip. As a result of fast development of tourism industry, commercial accommodations currently become wellknown in most areas, especially tourist destinations. There is close relation between size and categories of accommodation and location with the services supplied. Depend on the targeted consumers groups, the diverse services and amenities of accommodation facilities vary (Poudel, 2013). Tourist accommodation types can be classified by the following categories: hotels, resorts, motels, motor inns, rented apartments, guesthouses, bed and breakfast, backpackers, hostels, and caravan parks/camping grounds.

Future tourist accommodation demand forecasting
Establishment of modeling and forecasting is an important area in tourism and hospitality industry for their adequate future preparation. In recent period of time, researchers have paid even more attention to this potential sector. There has been a rise in the interest in forecasting the hotels demand based on hotel-specific data (Wu et al., 2017). The forecasts for future visitors' hotel demand will bring many advantages to hotel practitioners with the improvement in implementation of operational policy such as late cancelations, early departures, price discrimination, reservations by higher-value customers, overbooking policy (Wu et al., 2017). It is said that the hotel demand forecasting has also been used for future hotel business planning, hotel business operation management, planning for purchasing facilities to support hotel business operation and inventory management (Wu et al., 2017). The hotel accommodation demand could be determined by a variety of elements varying from different perspectives. The prediction of hotel demand for tourism industry is usually related to hotel revenue management (Wu et al., 2017). The profit of each available room as an aspect of financial performance, for instance, revenue earned per available room (RevPAR) and total sales revenue could be used to measure hotel demand. Many scholars stated that there are some elements related to the scale of hotel demand, such as the number of rooms served, guest arrivals, the number of nights guests stay, and occupancy rates of hotel (Wu, 2010). According Weatherford and Kimes (2003), the vital aspects of hotel revenue management is forecasting future occupancy rates and hotel guest arrivals and they stated that it is crucial to make the accurate forecasting which enable hoteliers to make the right decision to appropriately allocate hotel resources and modify pricing strategies. Yüksel (2007) applied a plenty of versions of exponential smoothing, as well as ARIMA and some Delphi methods aimed to forecast monthly hotel arrivals in a five star hotel in Ankara using 149 monthly series of data and made the comparison by using error measures the results with those from MA, Simple, Holt's, Winter's Exponential Smoothing and ARIMA. Another study is forecasting uncertain tourists accommodation demand in long term by applying and evaluating the Holt-Winters process, an extension of the exponentially weighted moving average (EWMA) (Rajopadhye et al., 2001). This aimed to forecast the uncertain demand for rooms at a hotel for each arrival day served by tourist accommodation by collecting data from past observation.

Previous hotel or tourist accommodation modeling and forecasting studies
Other scholars applied nonlinear time series models in the attempt to forecast tourism and hotel demand, such as the Markov-switching model and the self-exciting threshold autoregressive model. Rajopadhye et al. (2001) indicated that some scholars have applied the Holt-Winters method (a special version of the exponential smoothing technique) to predict hotel room demand each day in a specific property. They applied time series models to predict tourist accommodation demand in Kenya. The authors focused on the Box and Jenkins (1976) models to generate a forecasting model using quarterly data on bed occupancy rate by tourists coming to Kenya in the period of time from 1974 to 2011. Van Lohuizen and Smith (2017) used two different components -international visitor nights and domestic visitor nights. Forecasting hotel demand uncertainty (Ampountolas, 2018) was conducted by analyzing the average historical hotel data of nine hotels located in the city center of London with the usage of time series Bayesian VAR models -an econometrics instrument used for multivariate time series analyses. Other study is the application of the Box and Jenkins (1976) models and the twelve differenced SARMA (2, 2)(0, 2) which are considered as the optimal model to forecast tourist accommodation demand in New Zealand (Lim and Chan, 2009).

Grey system forecasting
The concept of the Grey system theory was founded by Julong D (1989) as a technique for conducting quantitative forecasting. Grey theory is well-known in academic environment for simple calculation and satisfactory outcomes.

Verhulst model
The Verhulst model was introduced by Pierre Franois Verhulst -a German biologist (Wang et al. 2009). The Verhulst model's main objective is to limit the entire growth for a system and it is efficient in the description of some increasing processes, for instance, an S-curve with a saturation region.

This is the Grey Verhulst model, and
(1) This is known as the whitenization equation of Grey Verhulst.

Theorem 3: The solution of equation (Verhulst 5) is
The time response sequence of the grey Verhulst model is:

ARIMA model
This model is based on the Box-Jenkins methodology (Box and Jenkins, 1976) as an appropriate technique for short term estimation based on hourly, daily, weekly, quarterly, annual data. The Box and Jenkins (1976) models are really well-known success in academic research and contribute significantly and successfully in forecasting (Chu, 2014).
ARIMA (autoregressive integrated moving average) is one of the most commonly used time series analysis model to predict the future values of a data sequence. Its primary application is utilized in the short term prediction area requiring at least 40 historical data points. The general model ARIMA (p, d, q) (P, D, Q) model can involve seasonal element of time series data analysis, it includes these primary parameters: p: the number of autoregressive terms q: the number of moving average terms d: the number of times a series P: the number of seasonal autoregressive components Q: the number of seasonal moving average terms D: the number of seasonal differences Here is a review of some of the types of nonseasonal ARIMA models that are commonly encountered is given below:  ARIMA (1, 0, 0)= first-order autoregressive model: This is an "ARIMA (1, 0, 0) + constant" model in which time series could be projected as a multiple of its own previous value plus a constant if it is stationary and auto-correlated. The forecasting equation in this case is Ŷt=μ+ϕ1*Yt-1 which is Y regressed on itself lagged by one period. If the mean of Y equals zero, then the constant term would not be added.  ARIMA (0, 1, 0) = random walk: This is the simplest possible model if the series Y is not stationary in which the autoregressive coefficient is equal to 1. It could be classified as an "ARIMA (0, 1, 0) model with constant" because it consists of (only) a non-seasonal difference and a constant term. The prediction equation for this model can be written as Ŷt=μ + Yt-1 where the constant term: the medium change from period to period in Y.  ARIMA (1, 1, 0) = differenced first-order autoregressive model: This is a first-order autoregressive model with one order of nonseasonal difference and a constant term. If the random walk model has auto-correlated errors, the problem might be fixed by the addition of one lag of the dependent variable to the prediction equation. This would be the following prediction equation: Ŷt=μ+ Yt-1+ϕ1 (Yt-1-Yt-2).  ARIMA (0, 1, 1) without constant = simple exponential smoothing: For some non-stationary time series, the random walk model does not perform well. In other words, this model uses an exponentially weighted moving average of past values to estimate more accurately the mean. The prediction equation for the simple exponential smoothing model can be written as Ŷt=Yt-1-(1α)*et-1=Yt-1-θ1et-1 with θ1= 1-α.  ARIMA (0, 1, 1) with constant = simple exponential smoothing with growth: It would cause some complications to apply the SES model as an ARIMA model. Firstly, the estimated coefficient of MA (1) is allowed to be lower than zero and as a result, a smoothing factor is higher than 1 in the SES model. This is usually not permitted by the SES model process. Secondly, there is an option of involving a constant term in the ARIMA model in order to assess an average non-zero trend. The prediction equation of ARIMA (0, 1, 1) model with constant is Ŷt=μ+ Yt-1-θ1et-1.  ARIMA (0, 2, 1) or (0, 2, 2) without constant = linear exponential smoothing: They are ARIMA models which use two non-seasonal differences in combination with MA terms. The second difference of a series Y at period t of the ARIMA (0, 2, 2) model without constant forecasts is equivalent to a linear function of the previous two forecast errors: Ŷt=2 Yt-1-Yt-2-θ1et-1-θ2et-2 in which θ1 and θ2 are the MA (1) and MA (2) coefficients respectively.  ARIMA (1, 1, 2) without constant = dampedtrend linear exponential smoothing: The forecasting equation of ARIMA (1, 1, 2) is Ŷt=Yt-1+ϕ1 (Yt-1-Yt-2)-θ1et-1-θ1et-1. It is commonly advised to apply this model in which at least one of two parameters p or q is no larger than 1.

Data collection and description
In this study, the researcher concentrates on predicting the demand of international and domestic tourist serviced by lodging sector in Lam Dong province, as well as total revenue generating from Lam Dong lodging activities in period of next 6 months.
In order to guarantee the proposed approach, the research collect and analyze monthly statistics which cover a period from January, 2012 to October, 2018 from official website of General Statistics Office of Lam Dong province and statistical yearbook of Lam Dong. The data were obtained from the website consist of Monthly Total Revenue from lodging services, International Tourists Serviced by tourism accommodations, Domestic Visitors serviced by holiday accommodation.
The group of domestic customers: for the general trend over time, the highest number of tourists served by holiday accommodations was the month during Lunar New Year (varying between January and February) and the summer time (from June to August) since people have holiday time during these time and the lowest months were March, April, September, October. In January 2012, the number of domestic equaled to 232,855 people which was much higher than the remaining months due to Lunar Tet Holiday. This number went down to 187,807 and 167,412 in February and March respectively. This number tended to improve from June to August which was all over 200,000 customers. During this time, students usually have summer time so this contributed significantly to the growth in number of domestic visitors. In the following year, domestic tourists in Tet Holiday in 2013, 2014, 2015, 2016, 2017, 2018 were respectively 273,812; 192,456; 208,800; 273,500; 295,300; 296,600. These statistics tended to be much lower in March every year. There were dramatic changes when it turned into summer time in which the number of visitors increased significantly from June to August. The most impressive change in this period of time is the increased approximately 97,000 from 208,845 visitors in May, 2013 to 304,673 in June, 2013 and went up more than 40,000 in July, 2013 (Fig. 3).

Fig. 3: Monthly number of domestic tourists serviced by holiday accommodation in Lam Dong
The group of international visitors: the number of tourists increased over time. However, the number of visitors has fluctuated every month. There is a different pattern in group of international tourists comparing to domestic group. They have been much higher at the end of each year starting from November to February of next year since during this time, the weather in many foreign countries become much colder than other months so that the foreigners usually found some places warmer to relax after a hard-working year. Seeing Domestic vitors from the graph, the statistics varied from under 10,000 to around 25,000 in the period of 49 months (January, 2012 to January, 2016). There was an impressive change in data of the remaining months when they tended to increase mostly over 25,000. The most dramatic number increased to the peak of 43,000 in February, 2018 and then went down with the high slope in the next following months (Fig. 4).

Fig. 4: Monthly number of international tourists serviced by holiday accommodation in Lam Dong
Total revenue generating from lodging activities: as we can see on the graph, total revenue from holiday accommodation sector in Lam Dong varied every month which were depended on the number of tourists serviced by lodging sector. The earning each month in 2012 was not over 2.5 million USD. From 2013 to 2017, the returns varied between 2.5 million USD to 3.5 million USD and at the end of 2017, it increased to the peak of 4.84 million USD.
Then the income from lodging activities went down to 3.33 million USD in January, 2018 and went up over 4 million USD for the rest of 2018 (Fig. 5).  Table 1 shows the description of statistics on the numbers of international and domestic tourists visiting to Lam Dong and total revenue gaining from tourist accommodations activities in Lam Dong. The mean of lodging earning, and the number of domestic and international visitors are 2.83; 245,514.1; 17,953.16 respectively. The highest value of domestic tourists is 401,000 and the lowest number is 141,515 while the maximum of international visitors equals to 43,000 and minimum is 5,270.

Data description and analysis
The accuracy of outcomes from the forecasting process is directly affected by the quality of the information and data collected. In the description part, the data were collected from January, 2012 to October, 2018 from the official website of General Statistics Office of Lam Dong. The number of international and domestic tourists serviced by tourist accommodation in Lam Dong fluctuates every month during this period of time. In general, the total number of tourists each year has increased significantly. In this part, we consider these following models to predict the tourist accommodation demand in Lam Dong based on the data collected from January, 2012 to October, 2018:    7533.6968, so the equation (0) (1)( 1 − 1) + 2 = 181338.0389.  Total revenue earned by tourist accommodation establishment: 1 = 1.0170; 2 = 1.7246, so the equation (0) (1)( 1 − 1) + 2 = 1.7538.  Table 2 and Table 3 are the outcome of analyzing results by applying ARIMA (0, 1, 1) (0, 1, 1), GM (1, 1), DGM (1, 1).

Accurate inspection analysis of forecasting ability
It is common to examine the forecasting accuracy by testing the difference between forecasts and the real value of demand among different models. There are a number of measurements for this assessment as follows. In the literature review, many scholars have concentrated on different ways to evaluate the accuracy of forecasting models' ability (Table 4). Accuracy evaluation components Song and Li (2008) The MAPE and root mean square percentage error (RMSE) to test the tourism demands forecasting ability Yüksel (2007) The MAPE, mean absolute deviation (MAD), and mean squared deviation (MSD) Rajopadhye et al. (2001) The MAD and the MAPE to measure the performance of the forecast ability Schwartz (1999) The MAD, MAPE, mean squared error (MSE), and standard deviation error (SDE) to monitor the accuracy of hotels' occupancy forecasts  The mean absolute percentage error (MAPE): One of the most common means is used to measure error which is popularly applied in forecasting. It is the average of the absolute percentage errors of forecasts. Error is expressed by actual value minus the forecasted value. Percentage errors are summed without regard to sign to compute MAPE. MAPE perform well to evaluate forecast error when the actual data has significant seasonality and demand fluctuates considerably from one period to the following period. The smaller the MAPE is, the more accurate the forecast is. MAPE is defined as follows: where At is the actual value and Ft is the forecast value. When MAPE is close to 0, the forecasting model is highly accurate and has provided good performance, and vice versa. Besides this, in accordance with the value of MAPE, the precision rate of forecasting model can be classified into four levels: excellent, good, qualified and unqualified (  Table 6 shows in details the criteria to evaluate the ability to forecast future demand. In this case, ARIMA (1, 1, 1) (1, 1, 1), is the only model shows a reliable way when their parameters of MAPE, MSE, RMSE and MAD are in the acceptable range. GM (1, 1), Verhulst and DGM (1, 1) are not chosen in this area because it perform poorly forecasting ability. Table 7 summarizes in details the parameter of MAPE, MSE, RMSE and MAD to evaluate the ability to forecast. The outcome shows that ARIMA (0, 1, 1) (0, 1, 1), is reliable model for forecasting demand of international customers. GM (1, 1), Verhulst and DGM (1, 1) are not ideal models in this field. Table 8 shows a comparison of four models to each other with four criteria, it is clear to see the "excellent" and "good" of evaluation of ARIMA (0, 1, 1) (0, 1, 1), GM (1, 1), DGM (1, 1) models to be chosen in forecasting tourist accommodation demand for total revenue generating from lodging activities. Verhulst are rated to be "reasonable".

Conclusion and discussion
Thus the objective of this study is to use the models of ARIMA, GM (1, 1), Verhulst, DGM (1, 1) to develop an easy and accurate way to forecast the demand for tourist accommodations. This study applies the parameter MAPE, MAD, MSE, RMSE to test which models can have better forecasting performance with the minimum projected errors. The forecasting outcomes show that some ARIMA models are good enough to the number of international tourists or domestic tourists of Lam Dong holiday accommodation industry since their MAPE, MAD, MSE, RMSE are reliable for the evaluation. In the case of revenue, ARIMA, GM (1, 1), DGM (1, 1) are appropriate methods with higher accuracy.
There are several practical implications from this study. Firstly, this study gives an overview about current situation in Lam Dong hotel industry. Secondly, it suggests an effective method for forecasting the domestic and international tourists accommodated by Lam Dong lodging sector and total return from the lodging sector investment.
Thirdly, in the case of the lodging revenue tend to continuously increase in the next half year, using the ARIMA, GM (1, 1), DGM (1, 1) models perform better than Verhulst. Besides that, for both international and domestic tourists, the application of ARIMA model works more effectively than the others. The research can conclude that ARIMA is applicable in forecasting these data sets.
Finally, the result provides an overall trend of the growth in number of tourists in the next 6 months which is grow slightly. Therefore, the governments must have some appropriate planning to balance the demand and supply and to guarantee the sanitation and quality of hotel industry satisfying tourists' requirements; enhance relative fundamental construction for hotel-related business markets; timely and synchronous adjustment in price system to increase the competition.