A Novel Hybrid Approach for Daily Tourism Arrival Forecasting: The PROPHET-Bayesian Gaussian Process-Forward Neural Network Model

Tourism has been identified as a major contributor to the economic advancement of numerous nations. Substantial research has been dedicated to forecasting tourism demand [1]. In particular, tourism serves as a cornerstone for Hawaii's economy. State government statistics revealed that the Hawaiian Islands were visited by more than 6.4 million visitors in 2003, with expenditures surpassing 10 billion dollars [2]. The dominant markets from which these visitors hailed included the United States of America (West and East), Japan, and Canada.

However, 2020 witnessed a drastic alteration in the global tourism landscape. The emergence of the COVID-19 epidemic profoundly affected Hawaii's tourism sector. Hawaii's initial case was reported in March 2020 [3]. Subsequently, the World Health Organization (WHO) categorized the outbreak of the novel coronavirus (2019-nCoV) as a global pandemic on March 6, 2020. Classified as a severe acute respiratory syndrome (SARS) variant, the coronavirus (COVID-19) was declared a pandemic by the WHO, underscoring its grave nature. The inaugural case was identified in December 2019 in Wuhan, China, as a novel viral pneumonia began affecting a cluster of patients. Following its identification, various precautionary measures were employed by governments globally to curb its proliferation. These measures encompassed containment strategies, prompt testing, mandatory mask usage, self-isolation, and the enforcement of social distancing. Notably, the countries most impacted encompassed the United States, India, Brazil, France, Germany, the United Kingdom, Russia, South Korea, Italy, Turkey, Spain, and Vietnam [4]. Global travel restrictions and lockdowns were imposed by January 2020 to thwart the spread of the SARS-CoV-2 virus, inducing a palpable shockwave through the global tourism and hospitality sectors. Such reverberations were profoundly felt in tourism-centric economies. In stark contrast to previous years, 2019's data showcased a plummet in Hawaiian tourist arrivals by 73.9%, resulting in a mere 2,708,258 visitors. Arrivals by air and cruise ship saw reductions by 73.9% (2,678,073 individuals) and 79.0% (30,185 guests) respectively. Consequently, the cumulative visitor days witnessed a 68.3% decline [2, 5].

The incorporation of Artificial Intelligence (AI) in predicting tourist arrivals is increasingly recognized as a revolutionary approach to a complex predicament. AI has been demonstrated to possess superior aptitude in deciphering intricate data patterns, discerning nonlinear relationships, and identifying dynamic shifts. The urgency to integrate AI into tourism forecasting is emphasized by its potential to amplify the precision and flexibility of predictions, notably in tumultuous periods exemplified by the COVID-19 outbreak. Nevertheless, such incorporations are not devoid of hurdles. Conventional forecasting techniques often wrestle with the intricacies presented by high-frequency data and multifaceted patterns. The pandemic’s pronounced disruptions have illuminated these predicaments, necessitating a profound reevaluation and recalibration of prediction models. This retooling is imperative to encapsulate rapid alterations in tourist behaviors, governance protocols, and health stipulations. Leveraging AI emerges as a prospective pathway to traverse these multifaceted challenges. Harnessing the power of AI facilitates a nuanced extraction of insights from expansive and variegated data pools, ultimately culminating in a more refined and adaptive forecasting strategy, especially amidst global uncertainties akin to the COVID-19 scenario.

DL has been extensively employed for predictive tasks, offering advancements over traditional AI models. Notably, most extant research has been oriented towards quarterly or monthly data, which, due to their low frequency, might provide limited insights. In contrast, daily data, given its higher frequency, is posited to furnish richer information. It has been confirmed by researchers that oscillations in tourist arrivals can be categorized into trends, irregularities, or seasonal components [6]. The complexity of forecasting daily tourist arrivals arises from the intricate interplay of linear trends and nonlinear patterns.

Predominantly, scholarly efforts have focused on leveraging diverse quantitative techniques, such as time series, econometrics, and AI, to forecast the volume of international visitors [6]. Within the domain of AI, neural network models have been discerned as potent tools for the tourism industry. It is acknowledged that DL falls under the umbrella of ML, which subsequently is a subset of AI. A salient feature distinguishing DL models from traditional neural networks is the heightened complexity, particularly in the depth of hidden layers within the neural architecture. In light of the COVID-19 pandemic's profound disruption of the tourism sector, there arises an imperative to estimate tourist flows using available pandemic-related data in tandem with inbound tourist statistics. A multitude of researchers and data scientists are engaged in the development of predictive models, aiming to elucidate the potential trajectory of the virus, which could serve to better forecast its proliferation [1].

Historically, the prowess of DL has been manifested in its adept handling of intricate data sets, exemplified in diverse studies such as face verification [7], Bitcoin price forecasting [8], and facial recognition [9]. This efficacy is largely attributed to DL's capability to autonomously discern and extract distinguishing features, obviating the necessity for extensive manual intervention or domain-specific knowledge. Yet, it is posited that solely relying on DL for forecasting tourist arrivals might be suboptimal, given the multifaceted nature of tourist arrival data. While Artificial Neural Networks (ANNs) are theoretically capable of modeling any nonlinear function with remarkable precision, they often encounter the pitfall of overfitting, leading to suboptimal performance. In this context, hybrid models emerge as promising solutions. Travel restrictions instituted in response to the COVID-19 pandemic have undeniably reshaped global tourism trends. Given the perceived superiority of daily data over lower-frequency data, daily tourist arrival statistics have been harnessed to craft daily forecasts. Consequently, a paramount research query is the development of a hybrid model that adeptly leverages time series data to refine the accuracy of tourist arrival predictions during the COVID-19 era. In addressing this, a linear technique amalgamated with nonlinear methodologies (PROPHET-BGP-FNN) is proposed. Challenges arise from mixed patterns in the data; while linear models often falter in modeling nonlinear patterns, their nonlinear counterparts are similarly encumbered when faced with linear patterns. This underscores the intricacy of effectively navigating data patterns that are interspersed with both linear and nonlinear elements. Notably, the trajectory of research in tourism prediction has seen the integration of time-series algorithms with both conventional neural network strategies and advanced DL methodologies.

In a comparative study conducted by Bouhaddour et al. [10], the SARIMA and PROPHET prediction models were evaluated for their capacity to forecast tourism in Singapore. These evaluations were based on historical tourist arrival data. While SARIMA is recognized for its proficiency in delineating both seasonal and non-seasonal patterns, the PROPHET model encompasses trend alterations and seasonality. Comparative metrics, such as mean absolute error (MSE) and root mean squared error (RMSE), were employed to gauge the forecasting performance. It was found that the PROPHET model exhibited superior forecasting capabilities compared to SARIMA. These findings hold significance, offering pertinent insights for refining tourism demand predictions, thereby aiding policymakers and industry stakeholders in their decision-making pursuits.

A distinct research endeavor led by Alamsyah et al. [11] delved into the application of ANN models for prognosticating tourism demand in Indonesia. The overarching objective was to augment the precision of tourism demand forecasts by harnessing the innate ability of ANNs to discern intricate patterns and nonlinear associations. Historical tourism data from Indonesia was utilized for training and assessment of the ANN models. Performance metrics such as mean absolute percentage error (MAPE) and RMSE were adopted to ascertain forecast accuracy. It was inferred that ANN models demonstrated commendable efficacy in prognosticating tourism demand, imparting valuable insights for strategic tourism planning in I MAPE Indonesia.

Wu et al. [12] proffered a novel forecasting methodology, amalgamating seasonal auto-regressive integrated moving average (SARIMA) with LSTM. This innovative approach was tailored for the prompt prediction of daily tourist arrivals in Macau SAR, China. LSTM, being a nonlinear AI methodology, is adept at encapsulating long-term contingencies in time series data. By synergizing the predictive prowess of SARIMA with LSTM's proficiency in residual reduction, the combined SARIMA + LSTM model was observed to eclipse other predictive techniques in efficacy. This research augments best practices in the tourism industry, particularly in terms of achieving precise daily arrival predictions.

Furthering the discourse, Assaf et al. [13] incorporated the Bayesian Global Vector Autoregressive (BGVAR) model for the formulation and prediction of regional tourism demand. The BGVAR framework integrates Bayesian statistical tenets and effectively captures interdependencies spanning multiple variables within a vector autoregressive (VAR) model. The deployment of the BGVAR model for regional tourism demand was undertaken with the intent to refine the accuracy and reliability of predictions.

Collectively, these studies underscore the continuous evolution and diversity of methods employed in tourism forecasting. Such advancements not only pave the way for enhanced predictive accuracy but also facilitate informed decision-making processes within the tourism industry.

In the extensive review of literature concerning proxies capturing tourism demand, the number of tourist arrivals was identified as the predominant variable employed. The discourse encompassed three principal methodologies utilized in the realm of tourist demand forecasting: econometrics, time series, and AI-based techniques. Nevertheless, in the present study, a composite model is introduced for forecasting tourist arrivals in Hawaii. Given that the time series of tourist arrivals manifests both linear and nonlinear characteristics, a composite prediction model, PROPHET -BGP-FNN, was constructed by integrating the PROPHET model, known for its adeptness at learning long-term historical data characteristics [14]. This hybrid model seeks to harness the advantages of the PROPHET model while preserving the predictive capabilities inherent to FNN-BGP models.

The impetus for this research has been shaped by the pressing demand for robust and adaptable forecasting instruments tailored for the tourism sector, especially in prominent destinations such as Hawaii. This urgency has been exacerbated by unforeseen disruptions, notably the COVID-19 pandemic. The envisaged practical ramifications of this research echo profoundly within the industry's recuperative endeavors. The composite forecasting model, PROPHET-BGP-FNN, is posited to equip stakeholders with an instrumental tool adept at anticipating the intricate vicissitudes in daily tourist arrivals. The pivotal applicability of this study is perceived in its prospective contributions to reinvigorating the tourism domain, accentuating its adaptability and resilience during periods characterized by flux and unpredictability.

Moreover, the efficacy of the PROPHET-BGP-FNN model in estimating the count of tourist arrivals is evaluated by contrasting its performance against that of four distinct models, notably SARIMAX, LSTM, and PROPHET.

The ensuing manuscript is systematically organized. Section 2 elucidates the methodology underpinning the proposed PROPHET-BGP-FNN model, supplemented by foundational knowledge. Section 3 delineates the process of data preparation, the model's implementation, and an analytical exploration of the empirical results garnered. Conclusions are drawn in Section 4.

3.1 Data preprocessing

For the purposes of this empirical investigation, real data concerning visitor arrivals were analyzed to assess the proposed model's performance. Hawaii was chosen as the subject of research due to its prominent global recognition as a leading tourist destination, experiencing consistent visitor inflows from across the world. This selection serves as a representative study for global tourism sites. Data pertaining to visitor arrivals across the four principal Hawaiian Islands was amassed for the period spanning January 1, 2017, to December 31, 2021. Figure 3 delineates the trends in visitor arrivals, and the associated descriptive statistics are encompassed in Table 1. Further insights into the flow of arrivals over this timeframe are visually represented in Figure 1, while Table 2 provides an in-depth statistical overview of the assembled dataset. Consequently, a total of 1824 observations for each origin were documented in the curated dataset.

Table 1. Descriptive statistics for daily tourist arrivals to Hawaii

Traditional methods were utilized to segregate the time series into discernible components for subsequent modeling. The primary components identified within the tourist demand data incorporated trends, seasonality, autocorrelation, cyclicality, and irregular patterns. These characteristics are broadly segregated into two predominant categories: a deterministic component exhibiting linear attributes and a stochastic component displaying non-linear attributes.

In the preliminary phase of this study, novel features were integrated into the dataset, aimed at enhancing the model's capacity to discern inherent patterns and interrelations. A prominent set of these incorporated features encompasses the mean and standard deviation computed over a rolling time window. These statistical attributes offer pivotal insights into data distribution, aiding the model in the identification and understanding of underlying trends and patterns. By assimilating this supplementary information, it is posited that the predictive accuracy and reliability stand to be heightened. This inclusion ensures the model's training encompasses data from both pre-pandemic and pandemic periods, facilitating a comprehensive understanding of COVID-19's impact on tourist inflows.

The engineering of features, specifically standard deviation and mean, remains a pivotal step in data analysis, as it contributes significantly to the enhancement of a model's accuracy, interpretability, and generalization. Through the extraction of these salient data attributes, deeper insights into the latent patterns and trends can be procured, thus informing decision-making based on the ensuing analyses. The data's distribution and central inclination are accurately represented by these statistics, with the standard deviation elucidating the data's variance and the mean approximating the data's central position. Typically, the derivation of standard deviation and mean proves instrumental in pinpointing potential outliers, evaluating data quality, and gleaning essential information for the modeling process. The formulae employed for the computation of mean and standard deviation are as follows:

Arithmetic mean $=\bar{x}=\frac{\sum_{i=1}^k x_i}{K}$       (4)

Standard deviation $=\sqrt{\frac{1}{k-1} \sum_{i=1}^K\left(x_i-\bar{x}\right)^2}$     (5)

K: Sum of all observation.

$x_i$: Observation.

When a feature's standard deviation is observed to be significantly large, it is indicative of a pronounced variation within the data. Such variation often necessitates additional pre-processing steps to achieve normalization of the distribution. Conversely, a diminutive standard deviation intimates that the data predominantly clusters around a central value, a factor instrumental in discerning patterns and facilitating predictions. The mean of a given feature can shed light on the data's archetypal or anticipated value, which subsequently can serve as a benchmark in evaluating performance.

Subsequent to these observations, the dataset was bifurcated to facilitate empirical analyses, resulting in distinct training and validation sets.

The PROPHET model was executed on Kaggle using the Python language, targeting a span of 10 months with a daily frequency. This dataset encompasses time series data for tourist arrivals in Hawaii. Through this method, seasonal patterns and variances in tourist arrivals over the stipulated 10-month duration were captured. Opting for a daily frequency permitted a granular scrutiny of the day-to-day fluctuations in tourist activities, revealing any persistent patterns characteristic to specific days. The primary objective of this implementation was to offer a holistic view of tourist influxes to Hawaii, emphasizing seasonal trajectories, pinpointing apex travel durations, and furnishing accurate prognostications for imminent arrivals.

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For the evaluation of the models discussed in this analysis, the metrics chosen were the Mean Absolute Error (MAE) and the MAPE. Their mathematical formulations are delineated in references [14, 21].

$M A P E=\frac{1}{N} \sum_{i=1}^N \frac{\left(\left|R_{v, i}-P_{v, i\,}\,\right|\right)}{R V} * 100$      (6)

$M A E=\frac{1}{N} \sum_{i=1}^N \frac{\left(\left|R_{v, i}-P_{v, i\,}\right|\right)}{N}$     (7)

$N$: Sum of all observation,

$R_v$: Reel value,

$P_v$: Predictive value,

The incorporation of error metrics, particularly MAE and MAPE, was deemed instrumental for a comprehensive evaluation of model performance. While MAE provides a straightforward quantification of the average discrepancies between predicted and observed values, serving as an indicator of prediction precision, MAPE presents a relative assessment by quantifying the mean percentage deviation between forecasted and actual outcomes, illuminating the comparative accuracy of predictions. These metrics together contribute to a discerning understanding of the predictive capabilities of the models, spotlighting their precision and elucidating errors in terms of both their magnitude and proportionality [22]. A graphical representation of MAE values can be viewed in Figure 4, aiding in a visual evaluation of model efficacy and predictive analysis.

Residuals were subsequently computed using the formula:

$R E=R_v-P_v$       (8)

where, $R_v$ denotes the actual value, $P_v$ signifies the forecasted value, and RE stands for the computed residuals. Following this initial phase, the modeling process transitioned to its second stage, in which the BGP-FNN method was employed for modeling the sequence of residuals. The objective function of BGP is perceived as a stochastic function with a Gaussian process distribution in an optimization based on the Gaussian process. A Gaussian process represents a collection of random variables, any finite number of which exhibit joint normal distribution. It is characterized by a mean function $m[x]$ and a covariance function $k\left[x, x^{\prime}\right]$, delineating the similarity between two distinct points. This Gaussian process is engaged in optimization to depict the distribution of objective function values across varying locales in the hyperparameter space.

A neural network architecture consisting of two hidden layers and a fully connected output layer was utilized. In the implementation of the BGP-FNN model, neurons in the first hidden layer ranged between 8 and 64, whereas the second hidden layer comprised between 2 and 16 neurons. The precise neuron count for the final model was determined by the BGP, which searched for the optimal combination of hyperparameters to enhance performance on the training data. Within the hidden layers of the neural network, a 'tanh' activation function, representing the hyperbolic tangent function, was adopted. Specifically, the first hidden layer of the BGP-FNN was configured with 36 neurons, while the second layer contained 16 neurons. The training process for the BGP-FNN was orchestrated using the 'Adam' optimizer, denoting the Adaptive Moment Estimation method.

For a comprehensive evaluation, the combined PROPHET-BGP-FNN model was benchmarked against SARIMAX, PROPHET, and LSTM models, each applied to the tourist arrival dataset. Table 2 offers a detailed juxtaposition of the results derived from LSTM, SARIMAX, PROPHET models, and the SARIMA–CNN–LSTM model.

A comparative assessment of the various forecasting models yields profound insights into their predictive competencies. The PROPHET-BGP-FNN model consistently demonstrated superior outcomes in terms of MAE and MAPE. Remarkably, as depicted in Table 2 and Figure 4, the MAE and MAPE values associated with the PROPHET-BGP-FNN model surpassed those of the PROPHET, LSTM, and SARIMA models. The efficacy of the PROPHET-BGP-FNN model can be attributed to its amalgamation of techniques. The foundational component, PROPHET, adeptly captures inherent seasonality and trends present in the time series data. Concurrently, the BGP-FNN excels at discerning intricate, nonlinear patterns in the dataset. This integration, complemented by Bayesian optimization, offers automated and efficient hyperparameter tuning, optimizing the model's performance.

While LSTM models, celebrated for their DL capabilities in time series forecasting, occasionally grapple with capturing complex patterns and mitigating vanishing gradients, the SARIMAX model, robust in addressing seasonality, sometimes falters in decoding non-linear patterns. Conversely, the PROPHET model, efficient in discerning seasonality and trends, witnesses performance augmentation when combined with the non-linear capabilities of the BGP-FNN.

In essence, the PROPHET-BGP-FNN model emerges as a paramount solution for forecasting tourist arrivals, combining the strengths of multiple techniques while adeptly navigating the intricacies of tourism demand data. The synergetic fusion in the PROPHET-BGP-FNN model—where Prophet discerns trends, BGP identifies non-linear patterns, and FNN perceives temporal dependencies—equips it to supersede the limitations inherent to individual techniques. Thus, it furnishes predictions embodying both deterministic and stochastic attributes of time series data, marking the PROPHET-BGP-FNN model as an innovative and reliable approach in forecasting tourist influx.

The amalgamation of PROPHET, BGP, and FNN within a cohesive framework highlighted the potential of model integration to address intricate forecasting challenges. Forecasts from both the hybrid PROPHET-BGP-FNN model and the standalone PROPHET model were subjected to tests, with the predictive outputs presented in Figure 5. In Figure 5, the blue solid line depicts the actual tourist count, while the orange and green lines represent the predictions derived from the PROPHET and PROPHET-BGP-FNN models, respectively. The horizontal axis marks the indices of the test data, and the vertical axis signifies the count of tourists. A comparison between predicted and actual tourist counts revealed an intrinsic capability of the model to discern non-linear characteristics within the data, thereby confirming its enhanced predictive potential.

Table 2. Comparative performance of various models

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Figure 4. Comparative MAE of distinct models

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In this study, an exhaustive suite of both traditional and advanced forecasting models was evaluated, culminating in the novel PROPHET-BGP-FNN model tailored for predicting tourist arrivals. The efficacy and limitations of each model were critically examined, with the PROPHET-BGP-FNN model emerging as the superior methodology. This superiority was further validated through its consistently lower MAE and MAPE values across diverse categories of tourist arrivals. Not only does the PROPHET-BGP-FNN model adeptly decipher deterministic and stochastic facets of time series data, but it also presents a pivotal solution for real-world applications.

For practical implications, the accurate forecasts provided by the PROPHET-BGP-FNN model have the potential to revolutionize decision-making processes within the tourism sector. Tourism agencies might leverage such precise predictions for a myriad of decisions ranging from resource allocation and staffing to formulating marketing strategies and infrastructure development. Furthermore, entities such as hotels, airlines, and other tourism-affiliated establishments could refine their operations predicated on projected tourist inflows, thus ensuring service excellence during high-demand seasons and circumventing excess capacity during off-peak times. By offering actionable insights, the PROPHET-BGP-FNN model stands poised to substantially elevate the operational efficiency and profitability within the tourism industry. In environments replete with challenges, high accuracy in predictions was achieved, underscoring the model's prospective utility in scenarios where precision in forecasting is of paramount importance for judicious decision-making.