Forecasting Destination Weekly Hotel Occupancy with Big Data

Abstract

Hospitality constituencies need accurate forecasting of future performance of hotels in specific destinations to benchmark their properties and better optimize operations. As competition increases, hotel managers have urgent need for accurate short-term forecasts. In this study, time-series models incorporating several tourism big data sources, including search engine queries, website traffic, and weekly weather information, are tested in order to construct an accurate forecasting model of weekly hotel occupancy for a destination. The results show the superiority of ARMAX models with both search engine queries and website traffic data in accurate forecasting. Also, the results suggest that weekly dummies are superior to Fourier terms in capturing the hotel seasonality. The limitations of the inclusion of multiple big data sources are noted since the reduction in forecasting error is minimal.

Keywords

tourism demand forecasting big data web traffic time series Markov switching dynamic regression model search engine query

Introduction

The value of accurate forecasting for tourist arrivals and hotel occupancy cannot be overstated (Song and Li 2008; Kim and Schwartz 2013; Schwartz and Hiemstra 1997). Accurate forecasting is a critical component of efficient business operations and destination management. Increasing competition and the adoption of revenue management practices have driven up the need for accurate forecasting in order to maximize profits and optimize operations in the hotel industry (Schwartz and Hiemstra 1997). In recent years, hoteliers have stressed the importance of short-term and high-frequency forecasting for the purpose of staying agile in a fiercely competitive marketplace (Hayes and Miller 2011).

At the destination level, if a hotelier can anticipate an increase or decrease in average hotel occupancy in one area, she or he can benchmark the property and make appropriate marketing or hiring decisions. However, hotel occupancy in high frequency and smaller geographic areas is always harder to predict (Yang, Pan, and Song 2014). Traditional forecasting methods include time series analysis, statistical methods, neural networks, pickup methods, and simulation (Law 1998; Song and Li 2008). No single method consistently outperforms other methods, and a combination of different forecasting models could perform better than an individual one (Palm and Zellner 1992). In addition, many of these methods use historical patterns to forecast future performance. This limits the accuracy of forecasting when the economic structure changes or unexpected events occur (Yang, Pan, and Song 2014). After researchers exhausted a variety of diverse models for experimentation, new types of predictors might be able to help further improve forecasting accuracy (Hubbard 2011).

Due to recent information technology advancements, researchers are now able to use the digital traces left behind by consumers to increase forecasting accuracy of many economic and social phenomena, including general economic indicators (Askitas and Zimmermann 2009), stock market movements (Bollen, Mao, and Zeng 2011), and election outcomes (Metaxas, Mustafaraj, and Gayo-Avello 2011). However, many scholars have also cautioned against becoming overly optimistic about the potential of forecasting using big data because quite often the accuracy is not as good as expected (Lazer et al. 2014).

In the field of tourism and hospitality, researchers have used data on Internet searches and web traffic volume to forecast tourist arrivals and hotel occupancy (Bangwayo-Skeete and Skeete 2015; Pan, Wu, and Song 2012; Yang et al. 2015; Yang, Pan, and Song 2014). Their results demonstrated the utility of different types of online data. However, no researchers have studied the effect of combined multiple data sources. One reason is that some big data sources might be correlated with each other. For example, searches on Google for a destination will be highly correlated with website traffic of that destination’s tourism bureau (Tierney and Pan 2012). Can multiple sources of big data be used to create a model that better predicts hotel occupancy?

In this study, we adopt multiple sources of big data and two different methods to forecast weekly hotel occupancy for one destination. The big data sources include related search engine queries, the local tourism bureau’s website traffic, and detailed weather information; the two different modeling techniques are autoregressive integrated moving average with external variables and a Markov switching dynamic regression model. The goal of the study is to explore the best way to predict the weekly hotel occupancy for one destination: What methods perform the best? Does using a combination of multiple big data sources significantly increase forecasting accuracy?

Literature Review

In this section, we first justify the rationale for adopting two different types of forecasting models; then, we review the techniques that are used to model seasonality in tourism demand; finally, we review recent literature on how big data are used to forecast economic and social phenomenon, including in the field of tourism and hospitality.

Different Models for Tourism Forecasting

Significant progress has been made in time series analysis of tourism demand over the last two decades (Peng, Song, and Crouch 2014). Peng, Song, and Crouch (2014) classified tourism demand forecasting models into five categories: basic time series models, advanced time series models, static econometric models, dynamic econometric models, and artificial intelligence models. According to this classification, major time series models include integrated autoregressive moving average (ARIMA) model, basic structural model (BSM) and structural time series model (STSM), generalized autoregressive conditional heteroskedasticity (GARCH) model, and long memory models. ARIMA models incorporate the autoregressive and moving average parts of stationary data (Kulendran and Wong 2005); BSM and STSM models analyze time series by estimating different components (Cortés-Jiménez and Blake 2011; Kulendran and Wong 2011); GARCH models capture the conditional variance (volatility) for exploring the effects of external shocks (Kim and Wong 2006); long memory models apply a fractional order of integration to the data to capture the long-range dependence in time series (Assaf, Pestana Barros, and Gil-Alana 2011).

Since some exogenous variables contain valuable information on future trends of tourism and hospitality demand, they can be used as predictors. Pure time series models can be modified to accommodate these external predictors: one of the most popular examples is autoregressive integrated moving average with exogenous input (ARIMAX) model, which extends the conventional ARIMA model by introducing additional independent variables (Yang, Pan, and Song 2014). Other popular econometric forecasting models with external variables as predictors include the autoregressive distributed lag model (ADLM), the error correction model (ECM), the vector autoregressive model (VAR) and the time varying parameter model (TVP) (Song and Li 2008).

Another model that has gained popularity in the tourism forecasting literature is the Markov switching dynamic regression model (MSDR), which assumes the transition of time series over a finite set of unobserved states with a random time of transition and duration of state. Many researchers have used MSDR models to unveil the cycles embedded in time series. This dynamic econometric model is also capable of capturing customers’ changing preferences over time (Li et al. 2006). By assuming that tourist markets are at different points of their lifecycles, Moore and Whitehall (2005) used a Markov switching model with a regime-dependent intercept to analyze quarterly tourist arrivals to Barbados from major source markets. Their results confirmed the different growth phases of different markets. Valadkhani and O’Mahony (2015) incorporated Markov switching components into their empirical model on inbound tourism demand to Australia. Likewise, Chen (2013) adopted a Markov switching model to investigate the tourist hotel industry cycle in Taiwan and described two regimes: high-growth and low-growth. Using a similar method, Chen, Wu, and Su (2014) and Chen, Lin, and Chen (2015) investigated the hotel business industry cycle and tourism market cycle. Applying such a model to tourism forecasting, Claveria and Datzira (2010) employed a Markov switching threshold autoregressive model as well as a set of other time series models to forecast international tourism demand in Catalonia with consumer confidence indicator as an additional predictor. They showed that ARIMA and Markov switching models are superior in general, and the latter outperforms other competitors in long-run forecasting (6–12 months in the future). Yang, Pan, and Song (2014) found that web traffic data, as a source of big data, is particularly useful in reducing forecasting errors during peak seasons, indicating different states with seasonality.

Researchers have not reached a consensus on the superiority of a single model across different scenarios (Witt and Witt 1995; Peng, Song, and Crouch 2014; Kim and Schwartz 2013). Among pure time series models, when no other predictors are available and the time series does not have any structural breaks, the ARIMA model family is recommended (Peng, Song, and Crouch 2014). Kim and Schwartz (2013) conducted a meta-analysis on the forecasting accuracy of various models, and found that the causal econometric model generally produces more accurate forecasts than pure time series models. Similarly, Peng, Song, and Crouch (2014) established a meta regression model to unveil factors explaining forecasting errors in the existing literature. The results showed that, after controlling for other factors such as origin, destination, time period, sample size, and demand measure, dynamic econometric model forecasts are associated with a lowest level of error. In addition, Li, Song, and Witt (2005) also found that dynamic econometric models outperform other forecasting models in many cases.

Hence, the results from these previous studies highlight the superiority of time series models and dynamic econometric model in forecasting tourism demand, but no model has been proven to be universally superior.

Dealing with Seasonality in Tourism Forecasting Models

A notable characteristic associated with tourism demand, seasonal fluctuations in quarterly, monthly and weekly data, can create difficulty in tourism forecasting (Song and Li 2008). Seasonality can be incorporated in the time series model in two ways, by either a stochastic method or a deterministic method (Kulendran and Wong 2005). To treat seasonality as a stochastic component, the data can be seasonally differenced (Kulendran and Wong 2005) or modeled using a state space form with a seasonal component (Song et al. 2011). For the deterministic method, a set of independent variables are included in the model. The most popular way is to introduce a set of dummy variables (Song and Li 2008). Another alternative is to incorporate trigonometric terms such as sine and cosine terms. For example, Stynes and Pigozzi (1983) used sine and cosine terms in their regressions to model seasonality in tourism employment. Chan (1993) showed that a sine wave time series regression generates more accurate forecasts than other models, such as the ARIMA. Wong (1997) found that a model with a linear trend and two sine functions outperforms other models in forecasting international tourist arrivals. Yang et al. (2014) incorporated the Fourier terms in their empirical model to test the stationarity of tourism demand in Taiwan. Apergis, Mervar, and Payne (2015) demonstrated that the model with Fourier transformation consistently outperforms others in forecasting tourist arrivals to different Croatian regions. Even though some statistical tests can be used to select between deterministic and stochastic methods in modeling seasonality, Kulendran and Wong (2005) showed that these tests may yield misleading results after evaluating the forecasting performance of different models.

Forecasting with Big Data

One can improve forecasting accuracy by adopting the winning model in the competition of many diverse models. However, once the competition reaches its limit, incorporating external predictors is a valid method to further increase forecasting accuracy. Recently, the so-called big data have emerged as powerful potential predictors. Big data refers to those data generated from human activity at volumes too large to be handled by traditional computing methods (Mayer-Schonberger and Cukier 2013). Today, travelers are continuously interacting with information technologies before, during, and after their trips. They search for information on the Internet, make purchases on websites, bring various gadgets with them on their trips, and record their experiences on social media. These interactions leave many types of digital traces that indicate their locations, spending habits, preferences and satisfaction. These valuable data include search engine queries, website traffic, transaction records, social media posts, and geographic locations. Many studies have been performed in different fields, including tourism and hospitality, on the predictive values of these big data sets. The following sections review a few.

Search Engine Queries

As a result of the large amount of information on the Internet, search has become the most popular online activity in the United States (Purcell 2011). Thus, one can use search engine query content and volume to understand and predict social and economic behavior. Researchers have used search engine query volumes to forecast disease outbreaks (Pelat et al. 2009; Helft 2008; Dugas et al. 2012; Valdivia and Monge-Corella 2010; Ginsberg et al. 2009; Althouse, Ng, and Cummings 2011), unemployment rates (Askitas and Zimmermann 2009), housing prices and sales (Wu and Brynjolfsson 2014), film revenues (Hand and Judge 2012), and tax evasion rates (Ayers, Ribisl, and Brownstein 2011). In the tourism field, Choi and Varian (2009) used the query tool Google Trends to forecast visitor volumes to Hong Kong; similarly, Gawlik, Kabaria, and Kaur (2011) forecasted tourism demand by proposing a query selection process. Pan, Wu, and Song (2012) used Google search data to forecast hotel demand for one destination; likewise, Yang et al. (2015) used Baidu query volumes to forecast the number of visitors to a province and achieved good results. Bangwayo-Skeete and Skeete (2015) adopted the Autoregressive Mixed-Data Sampling (AR-MIDAS) model, the Seasonal Autoregressive Integrated Moving Average (SARIMA) model, and the autoregressive (AR) approach to investigate the ways of incorporating search trend data into the forecasting of tourist arrivals in the Caribbean, and they demonstrated the superiority of the AR-MIDAS model. These studies have validated the value of using search engine query volume data as a powerful predictor for forecasting social and economic phenomena, including those related to tourism and hospitality.

Website Traffic

For many businesses and organizations, websites serve as virtual storefronts. A consumer will mostly likely visit a business’s website prior to making a purchase. Thus, the amount of visits to a website can indicate a business’s future revenue or performance. Web log software can help track visits to specific websites, through page-tagging or web server logs (Clifton 2010). Trueman, Wong, and Zhang (2001) used website traffic for many Internet companies from 1998 to 2000 to predict their revenue; likewise, Lazer, Lev, and Livnat (2001) found a significant correlation between the web traffic data of publicly traded Internet companies and their portfolio returns. In the field of tourism, Yang, Pan, and Song (2014) used a local destination marketing organization’s web traffic to forecast the average hotel occupancy of the area. They revealed that website traffic data increased the forecasting accuracy by 7% to 10%. Thus, as a precursor to purchasing activities, website traffic data can be a powerful potential predictor.

Weather Information

Weather and climate are crucial elements in the tourism industry (de Freitas 2003; Becken 2010). It can be a key attraction and also a necessary condition for travel. Thus, forecasted weather conditions could predict future visitor volumes (Frechtling 1996). Agnew, Palutikof and their colleagues (Agnew et al. 2006; Agnew and Palutikof 2001) discovered the correlation between weather conditions and travel demand. Specifically, outbound and inbound travel for British citizens is associated with different weather conditions, such as rain or snow, temperature, and the amount of days with sunlight. Álvarez-Díaz and Rosselló-Nadal (2010) used meteorological variables to predict outbound British visitors to the Balearic islands and achieved good forecasting results. They also found an impact of the North Atlantic Oscillation on domestic demand to Galicia, Spain (Otero-Giráldez, Álvarez-Díaz, and González-Gómez 2012). Similarly, snow conditions have been shown to forecast visitor volumes to ski resorts (Falk 2013). Falk (2014) modeled the impact of weather data on monthly overnight stays in several areas in Europe over 50 years. He found that the numbers of hours with sunshine and temperatures have a significant and positive impact on domestic visitor night stays. Multiple weather data were also adopted to forecast the travel population in three cities in South Korea, and different levels of forecasting accuracy were achieved (Lee et al. 2015). In general, weather data have become a significant data source which is useful for forecasting tourism demand.

In conclusion, the ARIMA series of models and the MSDR model have exhibited superior performance compared to other models. Fourier decomposition and dummy variables can be used to model seasonality in tourism demand fluctuations, especially for high-frequency data. In addition, big data sources, such as search engine queries, website traffic, and weather-related information could provide additional external variables for predicting hotel occupancy. However, to our knowledge, no known study has incorporated all the above methods and big data sources in a hospitality forecasting model. In this study, we combined different big data sources and the two aforementioned time series models based on Fourier decomposition or traditional weekly dummies to forecast weekly hotel occupancy for one destination.

Research Methodology

In order to assess the value of the two time series models and the efficacy of big data, we chose Charleston, South Carolina, in the United States as our test destination. Charleston is a historic city with around 800,000 residents living in the metropolitan area, and every year it attracts around 5 million visitors (Charleston Area CVB 2015). Located in the coastal area of South Carolina, it boasts a rich history from the antebellum era. We chose this destination because of convenient access to tourism demand data and big data sources related to the destination.

Two Forecasting Models

In this study, we tested two types of time series models and incorporated three big data sources to predict hotel occupancy. First we adopted the ARMAX models with big data–related variables as direct predictors. The ARMAX model extends the traditional ARMA model by including external variables as direct predictors. It can be specified as

\begin{array}{l} y_{t} = α + x_{t} β + μ_{t} \\ μ_{t} = \sum_{i = 1}^{m} ρ_{i} μ_{t - i} + \sum_{j = 1}^{n} θ_{j} ε_{t - j} + ε_{t} \end{array}

where y_t is the dependent variable, and $x_{t}$ is a vector of exogenous independent variables (which may include lagged variables). If β is set to 0, the model becomes a standard ARMA(m, n) model. Extensive efforts should be made to specify adequate m and n to guarantee that the model residual (ϵ_t) is white noise. To determine the lag length of independent variables, we selected the specification with the smallest value of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) (Liew 2004). Moreover, to capture the seasonality in the hotel demand embedded in the weekly data, we used two modeling methods: 1) the trigonometric representation of seasonal components based on the Fourier series (De Livera, Hyndman, and Snyder 2011); and 2) weekly dummy variables indicating the number of weeks in a year. The Fourier terms of sine and cosine pairs with varying periods have been accepted as a method to control for seasonal variation in the outcome variable (Harvey 1990). We introduced 24 trigonometric terms as the exogenous independent variable in $x_{t}$ , sin (2πjt/52.18), $\sin (2 π j t / 52.18),$ j = 1, …, 12 and cos (2πjt/52.18), $\cos (2 π j t / 52.18),$ j = 1, …, 12, as an approximation of seasonality. We used 52.18 since a year has an average of 52.18 weeks. For the second method of adding week dummies, the order of week is determined by the week’s starting date. Therefore, some years may consist of 53 instead 52 weeks, and in this case, we regard the 53th week as the 52nd when assigning dummy variables.

The second type of forecasting model used in this paper is the MSDR model. A general MSDR model is specified as

y_{t} = τ_{s} + x_{t} α + z_{t} β_{s} + ε_{s}

where $τ_{s}$ is the state-specific intercept; $x_{t}$ is a vector of exogenous variables (which may include lagged variables) with state-invariant coefficients; $z_{t}$ is a vector of exogenous variables (which may include lagged variables) with state-dependent coefficients $β_{s}$ ; $ε_{s}$ is an i.i.d. normal error with a mean of 0 and a state-dependent variance of $σ^{2}$ (Hamilton 1993). This model allows variables in $z_{t}$ with varying parameters across different states to accommodate structural breaks or other multiple-state phenomena, and these unobserved states follow a Markov process. In an aperiodic Markov chain with J states, p_ij indicates the transitional probability from stage i to stage j (j = 1,…, k), and is specified as follows:

\begin{array}{l} p_{i j} = \frac{1}{1 + \sum_{m = 1}^{k} \exp (- q_{i m})} if j = k \\ p_{i j} = \frac{\exp (- q_{i j})}{1 + \sum_{m = 1}^{k} \exp (- q_{i m})} if j \neq k \end{array}

where $q_{i j}$ is the transformed parameter specified as

q_{i j} = - \log (\frac{p_{i j}}{p_{i k}})

Note that seasonality terms (trigonometric terms or weekly dummies) are also included in $x_{t}$ as independent variables. To start the model estimation, an expectation–maximization (EM) algorithm is used to generate the initial value. After that, the estimation proceeds by predicting the probabilities of each state and updating the likelihood at each time (Hamilton 1993). A key step of this estimation is calculating the likelihood function of latent states, and this function is calculated by iterating the conditional likelihood.

To generate the out-of-sample forecasts, we used the one-step method to predict the value for the next week. For forecasts of 2 and more weeks ahead, we used the dynamic prediction strategy. In the ARMA/ARMAX model, a recursive prediction algorithm is used to predict dependent variable values for later time periods. In the MSDR model, a non-linear filter is used to predict the probability of a state conditional on previous states (Davidson 2004). In the tourism forecasting literature, it is a standard practice to benchmark the proposed model against a number of competing models (Song and Li 2008). Analyzing and comparing forecasting accuracy enables practitioners to choose the proper models. In this study, we focused particularly on (1) improving forecasting accuracy by including big data as predictors; (2) comparing the usefulness of two seasonality decomposition methods, Fourier terms and weekly dummies, for improving weekly forecasting accuracy; and (3) comparing the forecasting performance between the ARMA(X) and MSDR models. Two measures indicate the forecasting accuracy: mean absolute percentage error (MAPE) and the root mean square percentage error (RMSPE). They are specified as follows:

MAPE = \frac{1}{m} \sum_{t = 1}^{m} (\frac{| {\hat{y}}_{t} - y_{t} |}{y_{t}}) \times 100 %

RMSPE = \sqrt{\frac{1}{m} \sum_{t = 1}^{m} {(\frac{{\hat{y}}_{t} - y_{t}}{y_{t}})}^{2}} \times 100 %

To ensure the validity of the models, we split the data sample into two sub-samples: one for model estimation and the other one for forecast validation. Because of the remarkable seasonality in hotel demand, we suspected that the way in which the sample was divided could have impacted the evaluation of forecasting performance. Therefore, we performed 52 different splits to evaluate the forecasting performance throughout a year (m = 52 in equations (5) and (6)). The last 52 weeks of the data were used as the validation subsample for each split, and the data older than the validation subsample were regarded as the estimation subsample. It is of particular interest to understand the situations in which big data are more useful in reducing forecasting errors. We ran several auxiliary regression models to unveil the factors influencing the degree of improvement.

Data Description

In this study, we used average hotel occupancy in the Charleston area as the main time series. Smith Travel Research, Inc. (STR), collects performance data on hotel properties, aggregates them, and reports the summary and benchmarking data back to hotel properties. In the Charleston area, around 70% of hotel properties report their data to STR. Thus, their hotel occupancy rate can be considered a valid surrogate for the real hotel occupancy. STR provided weekly hotel occupancy data for Charleston County from week 1 of 2006 to week 30 of 2015.

There are three big data series we adopted as external variables. First, we used Google Correlate (http://correlate.google.com) to identify the most correlated queries with hotel occupancy series in Charleston County. Charleston hotels was the most highly-correlated and travel-related query. The other highly correlated queries, such as baseball pants or ditch witch were considered incidental. Thus, only search volume for Charleston hotels was used. The data series was normalized by Google with a mean of 0 and a standard deviation of 1. Second, we gathered weekly session data on website traffic for the Charleston Area Convention and Visitors Bureau (CACVB) website using Google Analytics, a free web log analysis tool provided by Google Inc. (Plaza 2011). A session is defined as a continuous period of access to the website from a visitor with less than 30 minutes between adjacent accesses. The web traffic data cover the time span from week 21 of 2007 (when the CACVB website installed Google Analytics) to week 30 of 2015 (the beginning of the research period). Third, we built a custom script in R language to download weather information from http://www.forecast.io. The weather data are based on public weather information gleaned from the National Weather Service for North America and Europe and thus can be considered accurate. We downloaded the daily data and aggregated them into weekly series that included the highest temperature, lowest temperature, average humidity, number of rainy days, and the number of snowy days.

Results

Table 1 presents descriptive statistics for the dependent and independent variables. The dependent variable is the weekly occupancy rate of Charleston hotels (occupancy). The variable search_engine is based on the Google Correlate data for Charleston hotels; the variable web_traffic is the number of sessions on the CACVB website in the week. For weather-related data series, after several preliminary runs of the forecasting model and controlling for seasonality, only the variable snowy_days (number of snowy days in a week) was found to be a valid predictor in some of the models.

Table 1.

Descriptive Statistics of Variables.

Variable	Period	Obs	Mean	Standard Deviation	Minimum	Maximum
occupancy	w1/2006-w30/2015	500	0.707	0.128	0.285	0.909
search_engine*	w1/2006-w30/2015	500	57.970	15.501	21	100
web_traffic**	w5/2008-w30/2015	391	41,458.010	14,103.170	13,858	78,054
snowy_days	w1/2006-w30/2015	500	0.008	0.109	0	2

Search_Engine is scaled search volume where the largest number in a time series is set at 100.

Web_traffic is the number of user sessions on Charleston Area Convention and Visitors Bureau website.

As shown in Table 1, during the study period, the average occupancy rate of Charleston hotels was around 70.7%, with a minimum of 28.5% and a maximum of 90.9%. Figure 1 presents the time series plots of the dependent variable and major independent variables, and these three series demonstrate very similar patterns of seasonal fluctuation.

Figure 1.

Time series plots of dependent and major independent variables.

Unit Root Tests

Before setting up forecasting models, we conducted two types of unit root tests, the Phillips-Perron (PP) test and the seasonal augmented Dickey-Fuller (ADF) test, to examine the stationarity of the major series. The results of both tests (Schwert 1989) suggested that the null hypothesis of non-stationarity can be rejected for all series, no matter whether a trend term is included (Table 2). Therefore, differencing these variables is not necessary.

Table 2.

Results of Unit Root Tests.

	PP Test Statistic		Seasonal ADF Test Statistic
Variable	Nontrend	Trend	Nontrend	Trend
occupancy	−6.955***	−6.969***	−6.207***	−6.233***
search_engine	−6.607***	−7.942***	−4.962***	−5.543***
web_traffic	−3.331***	−4.563***	−3.540***	−4.965***
snowy_days	−18.955***	−18.997***	−14.890***	−14.940***

Note: Lag number in unit root tests is determined by Bayesian information criterion values.

***

Significance at the 1% level.

ARMA/ARMAX Model Estimation

Table 3 presents the estimation results of the ARMA/ARMAX models. Following the recommendation by Athanasopoulos et al. (2011), we began by estimating pure time series models with extra independent variables. Model 1 is the ARMA model with Fourier terms (sine and cosine pairs), and Model 2 is the ARMA model with weekly dummies. The order of AR and MA terms was selected based on partial autocorrelation statistics and AIC/BIC values. An investigation of the residual correlation and normality diagnostics suggested that the residuals are white noise. As suggested by the lower AIC value of model 2, the inclusion of weekly dummies is superior than the Fourier terms in improving the model’s goodness of fit. However, according to BIC values, Model 1 is superior with a more parsimonious set of seasonality components. When considering additional exogenous independent variables in forecasting, we use both methods to capture seasonality. Because of space limitation, we present the results of weekly dummy models only (the estimation results of Fourier term models are available on request).

Table 3.

Estimation Results of ARMA/ARMAX Models.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
search_engine(L2)			0.000362			0.000434
			(0.000288)			(0.000399)
web_traffic(L2)				0.000000937**		0.000000858*
				(0.000000477)		(0.000000475)
snowy_days					−0.0327
					(0.0201)
constant	0.709***	0.381***	0.550***	0.542***	0.381***	0.721***
	(0.0165)	(0.0177)	(0.0302)	(0.0327)	(0.0177)	(0.0537)
AR(1)	−0.160***	0.0537	0.0546	0.161***	0.0619	0.159***
	(0.0420)	(0.0441)	(0.0442)	(0.0595)	(0.0442)	(0.0596)
AR(2)	0.306***	0.446***	0.442***	0.478***	0.455***	0.485***
	(0.0633)	(0.0891)	(0.0893)	(0.123)	(0.0903)	(0.117)
AR(3)	0.309***	0.131**	0.135**	0.0534	0.123**	0.0479
	(0.0426)	(0.0544)	(0.0546)	(0.0712)	(0.0543)	(0.0701)
AR(4)	0.473***	0.299***	0.303***	0.247***	0.292***	0.257***
	(0.0404)	(0.0556)	(0.0545)	(0.0707)	(0.0568)	(0.0689)
MA(2)	−0.355***	−0.380***	−0.397***	−0.403***	−0.383***	−0.432***
	(0.0772)	(0.0984)	(0.0996)	(0.126)	(0.0991)	(0.121)
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
σ	0.0393***	0.0357***	0.0355***	0.0311***	0.0355***	0.0310***
	(0.00132)	(0.00120)	(0.00119)	(0.00129)	(0.00118)	(0.00130)
N	473	473	471	362	473	362
AIC	−1656.1	−1693.5	−1689.5	−1366.7	−1696.7	−1366.4
BIC	−1527.2	−1452.3	−1444.4	−1137.1	−1451.3	−1132.9

Note: AIC = Akaike information criterion; BIC = Bayesian information criterion. Standard errors are presented in parentheses. L2 indicates the variable in a 2-week lag.

***

Significance at the 1% level; ^**significance at the 5% level; ^*significance at the 10% level.

To reach a parsimonious model, we introduced big data–related independent variables successively. As discussed previously, the selection of lag order of independent variables was guided by AIC and BIC values. For the ARMAX model, we found that a 2-week lag fits the data best. Model 3 is an ARMAX model with search_engine (in a 2-week lag) as an independent variable, and it is estimated to be insignificant. Model 4 considers web_traffic (in a 2-week lag), and this variable is estimated to be positive and statistically significant at the 0.05 level. We incorporated snowy_days in Model 5, and it is estimated to be insignificant, albeit negative as expected. In Model 6, both search_engine (in a 2-week lag) and web_traffic (in a 2-week lag) are included simultaneously, and only the latter is estimated to be marginally significant at the 0.10 level.

MSDR Model Estimation

Table 4 presents the estimation results of the MSDR models. Based on the results from preliminary modeling runs, we included two autoregressive terms, AR(1) and AR(2), to capture the dynamics of the dependent variables. The inclusion of more autoregressive terms in the MSDR model makes the optimization procedure hard to converge. Also, we specified only two states/regimes to avoid potential computational difficulties. Note that since the MSDR model is used for forecasting purposes, we are not interested in discussing the transition probabilities within the Markov process based on model estimates. Models 7 and 8 estimate the MSDR models without additional big data–related independent variables, and the former incorporates Fourier terms whereas the latter includes weekly dummies. Similar to the ARMA results, AIC/BIC values give conflicting results on selecting superior seasonality specifications. Because of space limitation, we present the results of weekly dummy models only (the estimation results of Fourier term models are available on request). In the MSDR models, the autoregressive terms and constant term are specified to vary across different states. Model 9 includes search_engine (in a 2-week lag), and its coefficient is estimated to be significant in both states. Based on AIC and BIC values, Model 9 is superior to Model 8. Model 10 incorporates web_traffic (in a 2-week lag) with state-dependent coefficients, and its coefficients are found to be significant and positive. In Model 11, the coefficient of snowy_days is also statistically significant and negative in State 2. Lastly, when both search_engine (in a 2-week lag) and web_traffic (in a 2-week lag) are considered in Model 12, these variables are estimated to be significant in State 1 only.

Table 4.

Estimation Results of MSDR Models.

	Model 7	Model 8	Model 9	Model 10	Model 11	Model 12
State 1
AR(1)	0.0105	0.589***	0.587***	0.361***	0.594***	0.303***
	(0.0542)	(0.0702)	(0.0696)	(0.0482)	(0.0698)	(0.0560)
AR(2)	0.240***	0.151***	0.124**	0.247***	0.155***	0.321***
	(0.0553)	(0.0573)	(0.0602)	(0.0472)	(0.0565)	(0.0555)
search_engine(L2)			0.000780**			−0.000633**
			(0.000320)			(0.000285)
web_traffic(L2)				0.000000851***		0.00000107***
				(0.000000173)		(0.000000226)
snowy_days					−0.0347
					(0.0223)
constant	0.552***	0.118***	0.105***	0.282***	0.114***	0.279***
	(0.0416)	(0.0290)	(0.0299)	(0.0210)	(0.0290)	(0.0228)
State 2
AR(1)	0.500***	0.0960*	0.177***	0.358***	0.0954*	0.703***
	(0.0541)	(0.0578)	(0.0549)	(0.114)	(0.0576)	(0.0836)
AR(2)	0.196***	0.449***	0.484***	0.360***	0.460***	0.0511
	(0.0481)	(0.0555)	(0.0537)	(0.104)	(0.0551)	(0.0729)
search_engine(L2)			−0.000933***			0.000253
			(0.000352)			(0.000403)
web_traffic(L2)				0.00000118**		0.000000265
				(0.000000571)		(0.000000388)
snowy_days					−0.0620**
					(0.0244)
constant	0.193***	0.290***	0.272***	0.133***	0.285***	0.126***
	(0.0397)	(0.0259)	(0.0254)	(0.0413)	(0.0257)	(0.0324)
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
σ	0.0382***	0.0338***	0.0330***	0.0271***	0.0335***	0.0275***
	(0.00169)	(0.00181)	(0.00145)	(0.00159)	(0.00178)	(0.00140)
N	471	471	471	362	471	362
AIC	−1493.9	−1593.3	−1604.3	−1315.4	−1596.5	−1315.1
BIC	−1356.8	−1344.0	−1346.7	−1074.1	−1338.9	−1066.1

Note: AIC = Akaike information criterion; BIC = Bayesian information criterion. Standard errors are presented in parentheses. L2 indicates the variable in a 2-week lag.

***

Significance at the 1% level; ^**significance at the 5% level; ^*significance at the 10% level.

Comparison of Forecasting Performance

Using the model specifications in Tables 3 and 4, we reestimated the model using a different estimation of subsamples from 52 data splits, and generated forecasts for the last 52 weeks in our original data set as ex ante forecasts. Because many of our forecasting models cover independent variables in 2-week lags, they are able to generate forecasts up to two steps only. We also assumed that it was possible to predict the number of snowy days that would occur within a 2-week period. The ex ante forecasting performance measures are presented in Table 5 (for MAPE) and Table 6 (for RMSPE). Also, we conducted the Diebold-Mariano (DM) test to compare the predictive accuracy of any two forecasting models (Diebold and Mariano 1995). The better-performing models are higlighted in italic in the table. Similar conclusions, described below, are reached if we use MAPE and RMSPE to select the best model.

Table 5.

Forecasting Performance (MAPE) of Models.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Big data predictor			a	b	c	a,b
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
MAPE (one-step)	4.276%	3.851%	3.804%	3.687%	3.879%	3.669%
DM test †	0.818		−1.0742	−0.745	0.307	−0.856
MAPE (two-step)	4.399%	3.860%	3.806%	3.716%	3.878%	3.698%
DM test †	0.969		−1.419*	−0.748	0.712	−0.851
	Model 7	Model 8	Model 9	Model 10	Model 11	Model 12
Big data predictor			a	b	c	a, b
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
MAPE (one-step)	7.159%	4.589%	4.714%	4.090%	4.642%	4.025%
DM test††	2.121**		0.446	−1.407*	0.764	−1.729**
MAPE (two-step)	6.962%	4.605%	4.480%	3.930%	4.586%	4.285%
DM test††	1.574*		−0.350	−2.437***	−0.531	−1.426*

Note: Smallest forecasting error in each row is underlined; a indicates search_engine(L2); b indicates web_traffic(L2); c indicates snowy_days.

†

Result compared to Model 2; ††result compared to Model 8.

***

Significance at the 1% level; ^**significance at the 5% level; ^*significance at the 10% level based on one-side test.

Table 6.

Forecasting Performance (RMSPE) of Models.

	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Big data predictor			a	b	c	a,b
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
RMSPE (one-step)	6.102%	5.018%	4.996%	4.787%	5.066%	4.781%
DM test†	1.441*		−0.837	−0.417	0.864	−0.533
RMSPE (two-step)	6.248%	5.015%	4.992%	4.821%	5.063%	4.809%
DM test†	1.497*		−0.829	−0.288	0.906	−0.434
	Model 7	Model 8	Model 9	Model 10	Model 11	Model 12
Big data predictor			a	b	c	a, b
Fourier terms	Yes	No	No	No	No	No
Weekly dummies	No	Yes	Yes	Yes	Yes	Yes
RMSPE (one-step)	13.251%	5.988%	6.053%	5.239%	6.001%	4.925%
DM test††	1.708**		0.820	−1.025	−0.0935	−1.526*
RMSPE (two-step)	13.459%	6.440%	5.966%	5.105%	6.406%	5.697%
DM test††	1.299*		−0.717	−1.826**	−1.1819	−1.627*

Note: Smallest forecasting error in each row is underlined; a indicates search_engine(L2); b indicates web_traffic(L2); c indicates snowy_days.

†

Result compared to Model 2; ††result compared to Model 8.

***

Significance at the 1% level; ^**significance at the 5% level; ^*significance at the 10% level based on one-side test.

First, models using weekly dummies (Models 2 and 8) outperform their counterparts incorporating Fourier terms (Models 1 and 7): the average MAPE and RMSPE values were reduced from Models 1 and 7 to Model 2 and 8, respectively, in both one-step and two-step forecasts. In particular, the DM test suggests that this improvement in accuracy is significant as measured by RMSPE in ARMA model or by both MAPE and RMSPE in MSDR models. Second, it shows that the combination of search query volume and web traffic data are particularly useful as indicated by the lowest MAPE and RMSPE values of Model 6 across all ARMA(X) models (Models 1–6) and that of Model 12 across all MSDR models (Models 7–12) for one-step forecasts. However, as indicated by the DM test, the forecasting accuracy of Model 6 is not significantly superior than that of Model 2 (without big data–related variables), but Model 12 generates significantly better forecasts than Model 7 (without any big data–related variables). Third, the MSDR model is slightly inferior to its counterpart, ARMA(X) model, in terms of forecasting accuracy. We find that the forecasting accuracy of Fourier term models is consistently inferior to the counterpart model with weekly dummies.

In general, as indicated by the results in Tables 5 and 6, Models 3, 4, and 6 outperform Models 2, and Models 10 and 12 outperform Model 8. This result highlights the usefulness of big data in improving performance accuracy. Compared to search_query, we found web_traffic to be more helpful in reducing forecasting error as indicated by the lower MAPE/RMSPE values of Models 4 and 10, as compared to Models 3 and 9. This result confirms the higher utility value of web traffic data in improving the forecasting accuracy of hotel demand. If both search_query and web_traffic are incorporated in the forecasting model, it generates the forecasts with lowest average errors. However, the two big data sources were estimated only significant in the inferior MSDR model (Model 12 in Table 4); only web traffic data was weakly significant in the best-performing ARIMAX model (Model 6 in Table 3).

Conclusion

The objective of the study is to investigate the best modeling technique for forecasting weekly hotel occupancy combined with big data sources. This study confirms the validity of two time-series models (ARMAX and MSDR) in forecasting a destination’s hotel occupancy rate (Song and Witt 2000; Chen, Wu, and Su 2014). Especially, ARMAX models generally perform better than MSDR models in forecasting accuracy in respective configuration, consistent with previous studies (Peng, Song, and Crouch 2014). Further, to capture the weekly seasonality in the hospitality time-series data, weekly dummies were found to outperform Fourier decomposition with sine and cosine terms. Combined, the ARMAX models with web traffic and search query volume information produce fairly accurate forecasts of average hotel occupancy for a destination one to two weeks in advance. The MAPE and RMSPE for out-of-sample forecasting could reach around 3.7% in both time periods for out-of-sample forecasts.

However, this study demonstrated the limitations of tourism big data. Even though search engine query volume and website traffic are good predictors that help reduce forecasting errors as shown in previous studies, the rate of error reductions is not as substantial as expected: the inclusion of two different data sources only decreases MAPE by around 0.2%, compared to the model with one source. A better ARMAX modeling configuration renders the value of big data insignificant: in the best ARMAX model, only website traffic data is marginally significant at 0.10 significance level; search engine query volume is not significant.

Regarding weather-related data, almost all series are nonsignificant in forecasting weekly occupancy. In one of the MSDR models, the number of snowy days was correlated with hotel occupancy and helpful in moderately increasing forecasting accuracy; however, over nearly 10 years, there were only 4 weeks with snowy days, since the destination is located in the southeastern United States where it rarely snows. The best models do not contain any weather-related series. Thus, weather information can hardly be described as effective in forecasting occupancy. This is different from previous studies in showing monthly weather-related information are correlated with tourism demand (Álvarez-Díaz and Rosselló-Nadal 2010; Agnew et al. 2006). The difference in this study might be due to the fact that travel decisions are usually made at least two or three weeks ahead (Yang et al. 2015). Current weather forecast is only accurate in at most five days to one week (Silver, 2012). Thus, the current weather can hardly impact the visitor volumes when they already made the destination choice or even reached their destination. This highlights the difficulty of short-term and high-frequency forecasting for tourism demand. This is also in line with recent studies showing the limitation of big data when Google Flu Trends project lost its accuracy because of changes in user behavior and search interface (Lazer et al. 2014; Hodson 2014).

In practice, one of the authors has been producing the weekly hotel occupancy and average daily rate forecasting for the Charleston area for almost a year with ARIMA models. The authors are working on incorporating big data and seasonality components to increase the forecasting accuracy. It is imaginable that other cities and areas with a strong seasonality could incorporate the methodology in this research into their forecasting practices. However, more diverse big data sets should be collected and integrated in order to further refine the forecasting models.

Discussion and Future Research

The first limitation of the study lies in the particularity of the single chosen destination. The destination is unique in that it has distinct seasonality patterns. Other destinations may exhibit irregular patterns that may decrease the efficacy of the methods. Second, the cost of configuring and running the model is rather high. Especially for the MSDR models, a personal computer with the current configuration would run for at least a few hours. Third, the big data we chose are also rather limited: we chose only one search query to represent search engine volume data. Although the query is the most correlated one, other nonobvious queries may contribute further to forecasting accuracy.

There are several opportunities for future research in this area. There has been much hype around the potential predictive power of big data in recent years. However, this study shows that big data sources do have limitations. Therefore, researchers need to seek diverse big data sources in order to further increase forecasting accuracy. For example, other big data sources that are very different from search engine queries and website traffic data, such as social media mentions or mobile phone data, could possibly yield more valuable predictors.

In addition, considering the actual needs of local hospitality establishments, forecasting extreme values is possibly more beneficial. For example, accurately forecasting a sudden drop in hotel occupancy due to severe weather or a dramatic increase due to an unexpected event would be extremely valuable to a hotel manager. Although extreme values (which might be outliers) would be more enlightening, MAPE or RMSPE only represent the average errors across the entire forecasting period. Using MAPE or RMSPE to measure model efficacy might not be appropriate, in which case other types of model fit measurements need to be researched and constructed.

Finally, it is most valuable when one can improve the forecasting accuracy of demand for a single property with big data. Tens of thousands of hotels in the United States could benefit from forecasting with increased accuracy because it could help them make better marketing or operational decisions. Working with individual properties and incorporating big data sources would be another fruitful research direction.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: this research is partially supported by National Natural Science Foundation of China with grant No. 41428101.

Author Biographies

Bing Pan, PhD, is associate professor in the department of Recreation, Park, and Tourism, College of Health and Human Development, Penn State University. His research interests include information technologies in tourism, destination marketing, and search engine marketing.

Yang Yang, PhD, is assistant professor in the School of Sport, Tourism and Hospitality Management at Temple University. His areas of research interest include tourism demand analysis and location analysis in the hospitality and tourism industry.

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