Urban tourist volume forecasting using internet search trends and deep learning methods

Abstract

Accurate forecasting of tourist arrivals in major urban destinations is critical for optimizing tourism resource allocation and formulating data-driven marketing strategies. To address this need, this study presents a novel prediction framework that integrates deep learning methodologies with online search behavior data. Specifically, we propose the DTN (Dynamic Tourism Network) model, which combines Disentangled Shape and Time series Normalization (Dish-TS) with Temporal Convolutional Networks (TCN), and utilizes Baidu Index data as a key indicator of online search trends to predict tourist arrivals in Sanya, China. Empirical validation across multiple evaluation metrics demonstrates that the DTN model consistently surpasses conventional deep learning approaches, achieving statistically significant improvements in predictive accuracy for tourist volume estimation. This advancement provides a robust analytical foundation for real‑time tourism demand forecasting in destination management systems. Notably, the proposed method has been evaluated only on a popular urban tourist destination with pronounced seasonality and available Baidu Index data; its applicability to other destination types or regions where different search engines dominate therefore requires further validation.

1. Introduction

With rapid socio-economic development and increasingly diversified population needs, the strategic importance of tourism in national economies worldwide has grown substantially (Schrader et al., 2025; Zhou and Zhuang, 2025). Tourism not only enhances public quality of life but also generates considerable economic benefits for regions and serves as an important driver of local economic growth. Therefore, accurate forecasting of tourism demand—specifically tourist volume—for a city is crucial for the rational planning of tourism resources, optimization of tourism facilities, and formulation of effective marketing strategies.

Traditional methods for forecasting tourism demand primarily rely on historical data, such as time-series data on tourist numbers and tourism revenue, using statistical models for prediction. However, these methods often fail to account for the speed and real-time nature of information dissemination in the Internet era. The prevalence of the mobile Internet enables people to obtain abundant information about tourism destinations through search engines before traveling, and the specific keywords searched reflect potential tourism demand. Therefore, analyzing the relationship between mobile Internet search trends and tourism demand provides new perspectives and methods for tourism demand forecasting.

However, existing research utilizing online search data for tourism forecasting continues to face multi-dimensional challenges. At the data level, search engine data (e.g., Baidu Index) is often characterized by high-dimensional noise and stochastic volatility. Prevailing methods, which typically employ raw data or linear dimensionality reduction, fail to effectively filter out noise and distinguish the differential predictive signals between mobile and PC search platforms. At the model level, despite the introduction of advanced architectures such as Temporal Convolutional Networks (TCNs), Spatio-Temporal Graph Neural Networks (ST-GNNs), and attention mechanisms (Lea et al., 2017 and Hadou et al., 2022), their application to specific cities like Sanya remains limited. TCNs exhibit limited capacity for disentangling multi-scale seasonal features; ST-GNNs demand high data quality and volume while offering insufficient interpretability; and RNN-based models still have room for improvement in adapting to sudden demand shocks. More critically, few studies have systematically decoupled the shape and periodic characteristics of time series or deeply integrated denoised mobile search trends into a framework that combines long-term dependency modeling with high interpretability. This gap hinders the achievement of accurate, real-time, and reliable forecasts for specific tourist destinations, ultimately limiting the model’s dependable application in scenarios involving demand surges during holidays or emergent events.

Therefore, this study aims to address these limitations by proposing a novel deep learning-based forecasting framework. We introduce the DTN model, which integrates Dish-TS with TCN, using Baidu Index data as a core indicator of search trends. Our objective is to enhance the accuracy, robustness, and interpretability of tourist volume predictions for urban destinations, thereby providing a more reliable analytical tool for tourism management and strategic planning.

It should be noted that this study focuses on Sanya, a representative coastal tourism city in China, as the empirical case. The choice of Sanya is motivated by its strong seasonal tourism patterns, high penetration of Baidu search engine usage, and data availability. Consequently, the proposed DTN model is primarily applicable to urban destinations that exhibit similar characteristics, such as pronounced periodicity and access to reliable Baidu Index data. Generalization to other geographic contexts (e.g., international destinations using Google Trends) or tourism types (e.g., heritage or ecotourism sites) requires further investigation.

The specific methodological contributions of the proposed DTN framework are threefold. First, unlike conventional normalization techniques (e.g., batch normalization or instance normalization) that treat time series as independent samples, Dish-TS disentangles shape and temporal features through learnable local statistics, enabling adaptive normalization that preserves seasonal patterns while removing non-stationary drift. Second, while existing hybrid models use autoencoders for dimensionality reduction followed by recurrent networks for prediction, our framework integrates normalization and temporal convolution in an end-to-end trainable pipeline where Dish-N and Dish-D are optimized jointly with the TCN. Third, to the best of our knowledge, this is the first study to combine Dish-TS with TCN for tourism demand forecasting, offering a lightweight yet powerful alternative to attention-heavy architectures such as TFT (Lim et al., 2020) or Transformer-based models. These contributions position the DTN as a novel approach that balances predictive accuracy, interpretability (via adaptive weighting of holiday-specific features), and computational efficiency.

2. Related work

2.1. Tourism demand forecasting methods

Tourism demand forecasting has long been a key concern in both academia and industry. The primary methodologies employed include time series analysis, regression analysis, econometric modeling, and deep learning approaches.

2.1.1. Time series analysis

This approach models the temporal characteristics of historical data to predict future trends, often employing techniques such as the Autoregressive Integrated Moving Average (ARIMA) model (Box et al., 2015). A standard ARIMA (p, d, q) model, after differencing the series $d$ times to achieve stationarity, can be expressed for the stationary series $Y_t$ as:

$$Y_t=\sum _{i=1}^p{\varphi }_i{Y}_{t-i}+\sum _{j=1}^q{\theta }_j{\in }_{t-j}+{\in }_t$$

where $Y_t$ denotes the value of the time series at time $t$ , ${\varphi }_i$ and ${\theta }_j$ are the autoregressive and moving average coefficients, $p$ and $q$ are the autoregressive and moving average orders, respectively, and ${\in }_t$ is a white noise error term. A key limitation of this method is its strong reliance on the assumption of data stationarity, rendering it less adaptable to sudden disruptions—such as natural disasters or policy changes—that violate this assumption and degrade forecast performance.

2.1.2. Regression analysis

This method explores the linear relationship between tourism demand and various influencing factors (Crouch et al., 1992). These factors encompass economic indicators (e.g., disposable income, GDP growth rate), social factors (e.g., demographic structure, education level), and environmental factors (e.g., temperature, air quality). Forecasting is performed by constructing a regression equation of the general form:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_n{X}_n+\in$$

where $Y$ represents tourism demand, $X_i$ denotes the $i$ -th influencing factor, ${\beta }_i$ is the corresponding regression coefficient, and $ϵ$ is the error term. Research indicates that incorporating factors such as local economic development level and transportation accessibility into a regression model can effectively explain variations in urban tourism demand. A key limitation of this approach is its assumption of a linear relationship between each predictor and the response variable. In reality, these relationships are often complex and nonlinear. Furthermore, variable selection relies heavily on domain expertise, which may lead to the omission of key factors or the inclusion of redundant variables, thereby compromising the model’s accuracy and explanatory power.

2.1.3. Econometric model

These models integrate economic, social, and other factors to forecast tourism demand by constructing systems of simultaneous equations (Ni et al., 2018). However, their specification and parameter estimation processes are complex and place high demands on data quality.

2.1.4. The gray system

The gray system model is suitable for forecasting with limited data and incomplete information, and is commonly applied to predict demand for emerging destinations or niche tourism products (Liu et al., 2014). It constructs a new sequence by accumulating the original data to weaken random noise and uncover underlying patterns. For instance, for a newly developed tourism route with scarce historical data, the Gray GM (1, 1) model can utilize limited information such as initial booking data and marketing inputs to provide a preliminary forecast of market demand trends, aiding decision-making for tourism enterprises. However, the gray model’s capability for long-term trend prediction is relatively weak, and its accuracy is highly sensitive to the dispersion and smoothness of the original data. This sensitivity limits its predictive performance when data quality is poor.

2.1.5. Deep learning approaches

With the rapid advancement of big data and artificial intelligence technologies, deep learning has become a prominent approach in tourism demand forecasting due to its powerful nonlinear modeling capabilities and automated feature extraction. Unlike traditional models that rely on strong assumptions, deep learning models can autonomously learn complex patterns from high-dimensional data—such as internet search indices and multi-source spatiotemporal data—significantly enhancing prediction accuracy and adaptability. Recent research has primarily focused on innovations in the following model categories:

• (1) Temporal convolutional networks and their variants

TCNs have garnered significant attention in tourism forecasting due to their ability to effectively capture long-term dependencies through causal and dilated convolutions while maintaining structural stability and avoiding the gradient issues common in recurrent neural networks. For example, research has applied the multi-objective genetic algorithm NSGA-III for feature selection, constructing TCN models for hotel demand forecasting that enhance predictive performance while reducing complexity (Park et al., 2024). More advanced developments integrate TCNs with spatial modeling to address interactions among multiple destinations. The Dynamic Spatio-Temporal Convolutional Network (DSTCN) represents a key development in this direction (Pan et al., 2025). This model employs Graph Convolutional Networks (GCNs) to capture dynamic spatial dependencies between attractions while utilizing TCNs to extract heterogeneous temporal features for each node. By effectively integrating dynamic spatio-temporal information, DSTCN demonstrates superior performance across various temporal granularities.

• (2) Spatio-temporal graph neural networks

To explicitly model the spatial diffusion and network effects of tourism flows, researchers have introduced graph neural networks. These approaches treat tourist destinations as nodes in a graph, with spatial relationships (e.g., geographic adjacency, visitor flows) represented by edges. For instance, a recent study proposed a framework integrating spatio-temporal Generative Adversarial Networks (GANs) with an enhanced Transformer (Diao et al., 2025). This framework employs a generator with graph convolutions to dynamically generate virtual samples, mitigating data scarcity. It uses a Transformer augmented with causal convolutions as a predictor to capture multi-scale dependencies, achieving precise predictions in small-sample scenarios.

• (3) Hybrid frameworks for dimension reduction and prediction using search engine data

While providing abundant information, search engine data poses challenges of high dimensionality, noise, and redundancy. To address this, one study proposed a two-stage deep learning hybrid framework (SAE-Bi-GRU) specifically designed to process such data for tourism forecasting (Li et al., 2022). In the first stage, a Stacked Autoencoder (SAE) performs nonlinear dimensionality reduction on raw Baidu Index and Google Trends data. Compared to linear methods like Principal Component Analysis (PCA), SAE more effectively extracts key predictive features from high-dimensional noisy data. In the second stage, a Bidirectional Gated Recurrent Unit (Bi-GRU) network models the reduced features alongside historical visitor flow sequences. Its bidirectional architecture captures both forward and backward temporal dependencies. Empirical results show that the SAE-Bi-GRU framework achieves higher prediction accuracy than benchmarks using PCA for dimensionality reduction, as well as traditional models like SARIMA and Support Vector Regression (SVR).

• (4) Recurrent neural networks integrating multi-source data with attention mechanisms

A key advantage of deep learning is its capacity to effectively integrate and weight predictive variables from diverse sources. Research proposed an Attention-based Bidirectional Long Short-Term Memory (ATT-BiLSTM) model for the Jiuzhaigou Scenic Area (Han et al., 2023). This model integrates historical visitor flow data, Baidu search indices, multi-dimensional weather data, and holiday information. An attention mechanism automatically assigns differentiated weights to input features based on their contextual importance, enabling more precise extraction of key information. This work highlights the value of adaptive feature weighting and multi-source data fusion in complex forecasting tasks.

• (5) Innovative approaches based on data augmentation and feature decoupling

To address challenges of data sparsity and entangled feature representations, recent research explores innovations at both data and feature levels. Beyond GAN-based sample generation, feature disentanglement learning has shown promise. For example, one study constructed spatio-temporal graphs across user sequences to decouple spatial and temporal influences in group movement patterns toward destinations (Zeng et al., 2025). This approach learns purer, more interpretable feature representations, enhancing prediction accuracy.

In summary, current deep learning-based tourism forecasting research is evolving from simple time-series modeling toward complex frameworks that integrate spatio-temporal dynamics, multi-source data fusion, and small-sample learning techniques. These methods provide powerful tools for addressing the nonlinearity, volatility, and spatial correlations inherent in tourism demand. Developed within this context, the DTN model proposed in this study aims to more precisely decouple the shape and temporal characteristics of time series while deeply integrating internet search behavior—a key leading indicator—to further enhance prediction accuracy and robustness.

2.2. Application of internet search data in tourism demand forecasting

In recent years, the increasing availability of internet data has led to its widespread application in tourism demand forecasting. Search engine query data can serve as a proxy for user interest and attention toward tourism destinations, showing a significant correlation with actual tourism demand (Song et al., 2019). Numerous studies demonstrate that predictive accuracy can be effectively improved by incorporating search data from platforms such as Google Trends and Baidu Index into machine learning and deep learning models (Li et al., 2017; Li et al., 2018). For example, analyzing fluctuations in the search volume for keywords related to a specific destination can provide early signals of shifting demand, offering valuable insights for tourism management and business strategy. However, research focusing on tourism demand forecasting for Sanya remains relatively scarce, particularly studies that deeply integrate mobile internet search trends.

Deep learning algorithms, when applied to Baidu Index data, leverage their strengths in nonlinear modeling and automatic feature extraction to uncover latent patterns in tourist behavior and preferences embedded within search data, thereby enhancing prediction accuracy and robustness. Compared to traditional linear models, deep learning approaches can capture complex features such as keyword co-occurrence and temporal search sequences, leading to more intelligent and precise demand forecasts.

While the above-reviewed studies demonstrate the value of integrating search engine data with deep learning models, many of them, including the present work, rely on a single destination case (e.g., Sanya) for empirical validation. Single-case study designs are common in early-stage methodological research as they allow for in-depth analysis and control of destination-specific confounding factors. However, they inevitably raise questions about the robustness and generalizability of the proposed models across different tourism contexts. The predictive performance observed in one city may not directly transfer to destinations with different seasonal patterns, search behavior cultures, or data quality. Therefore, findings from single-destination studies should be interpreted as proof-of-concept evidence, and multi-destination benchmarking is necessary to establish the broader utility of any newly proposed forecasting framework.

While the hybrid frameworks reviewed above have advanced tourism demand forecasting, the proposed DTN model differs in several key aspects. First, unlike SAE-Bi-GRU, which applies a stacked autoencoder for nonlinear dimensionality reduction separately from the recurrent predictor, DTN integrates Dish-TS normalization directly into the TCN backbone, allowing the normalization parameters to be learned end-to-end with the forecasting objective. Second, whereas ATT-BiLSTM relies on attention mechanisms to weight input features adaptively, DTN achieves adaptive feature weighting through the learnable statistics of Dish-TS and the dilated convolutions of TCN, without introducing quadratic complexity. Third, compared to DSTCN, which focuses on spatio-temporal dependencies across multiple attractions, DTN is specifically designed for univariate tourist volume prediction with exogenous search data, emphasizing the disentanglement of shape and periodic components. Fourth, while TFT and N-BEATS (added as baselines in this study) are powerful general-purpose forecasters, they either require static covariates (TFT) or do not natively handle exogenous variables (N-BEATS; Oreshkin et al., 2020). DTN, by contrast, seamlessly incorporates multi-dimensional Baidu Index features as exogenous inputs while preserving interpretability through its separate normalization and denormalization modules. Therefore, the DTN occupies a distinct niche: a lightweight, interpretable, and end-to-end framework that couples adaptive normalization with temporal convolution for tourism forecasting with search engine data.

3. Research methodology

3.1. Data sources

The search data for this study were sourced from the Baidu Index platform. As the world’s largest Chinese-language search engine, Baidu covers a comprehensive demographic across various ages, regions, and industries. Its Index aggregates multi-dimensional information, including keyword search volume, market demand, and user characteristics (Huang et al., 2017).

This study focuses on Sanya, a renowned coastal tourism city in China. We selected a set of keywords closely related to Sanya’s tourism sector, including “Sanya tourism” (三亚旅游), “Sanya attractions” (三亚景点), “Sanya hotels” (三亚酒店), “Sanya food” (三亚美食), and “Sanya travel guide” (三亚旅游攻略). Using these keywords, we collected the daily search index data for both PC and mobile platforms from January 2012 to October 2019.

The collected dataset comprises monthly tourist arrival records for Sanya covering the same period (January 2012 to October 2019), yielding a total of 94 monthly observations. After preprocessing and alignment with the Baidu Index data, the final time series consists of 94 data points for each of the 14 candidate keywords and the tourist arrival series. The dataset was partitioned into training, validation, and test sets using a 70:15:15 ratio, resulting in 66 training samples, 14 validation samples, and 14 test samples (see Section 4.1 for details on the sliding window generation). The main statistical properties of the tourist arrival series are as follows: mean = 1,377,946 visitors per month, standard deviation = 426,884, minimum = 637,600 (June 2012), and maximum = 2,668,000 (December 2018). The series exhibits moderate positive skewness (0.60) and slight platykurtic distribution (−0.03 excess kurtosis), indicating a non-normal distribution with occasional extreme peaks during holiday periods.

3.2. Correlation analysis of tourist arrivals

A correlation analysis was performed on the monthly tourist arrivals data for Sanya. The resulting autocorrelation function (ACF) plot is presented in Figure 1. The ACF plot reveals several key characteristics:

Figure 1.

ACF of monthly tourist arrivals in Sanya.

• (1) Pronounced seasonal pattern: The ACF exhibits a significant peak at lag 12 that extends beyond the 95% confidence interval, indicating a strong annual periodicity corresponding to recurring tourism peaks (e.g., winter holidays). However, the autocorrelation at lag 24 falls below the confidence bounds and is lower than the value at lag 11. This pattern suggests that while the 12-month seasonal cycle is dominant, the 24-month lag does not maintain the same level of correlation, implying that the seasonal effect may decay or be modulated by year-specific factors (e.g., policy changes or major events). Therefore, the seasonal pattern is best characterized as a 12-month periodicity with diminishing second-order seasonal dependence.

• (2) Long-term persistence: The autocorrelation coefficients decay gradually as the lag order increases, suggesting that historical values exert a prolonged influence on future ones, which may imply the presence of a trend or long-range dependence.

• (3) Short-term correlation: The autocorrelation coefficients at lags 1 and 2 are high and statistically significant, indicating a direct correlation between tourist volumes in consecutive months.

To achieve stationarity, first-order differencing and seasonal differencing were applied to the original time series. The results are shown in Figure 2. The ACF plot of the differenced series and the corresponding statistical test results (Table 1) show that most autocorrelation coefficients fall within the 95% confidence interval (the blue shaded area). This indicates that the series is approximately stationary after differencing, confirming that the differencing operation effectively removed the non-stationary trends.

Figure 2.

Schematic of the autocorrelation of the number of tourists in Sanya after first-order differencing and seasonal differencing.

Table 1.

Data test results before and after differencing.

ACF type	ADF statistic	p-value	Critical values
			1%	5%	10%
ACF	−2.027	0.275	−3.476	−2.882	−2.578
ACF after Differencing	−4.754	6.658e-5	−3.482	−2.884	−2.579

3.3. Baidu index data processing and keyword selection

Following data cleaning procedures, including duplicate detection and outlier correction, the Baidu Index dataset was temporally aligned with the tourism demand series. The Baidu Index data are recorded at a daily frequency, whereas tourist arrivals data are aggregated monthly. To synchronize these datasets, the daily search indices were resampled to monthly intervals by calculating the mean value for each month.

The Baidu Index is organized around search queries, yielding a large set of keywords related to “Sanya Tourism.” To identify the most relevant predictors, a keyword filtering process was implemented. Fourteen representative keywords were initially selected (Table 2), and their corresponding Baidu Index time series were retrieved and preprocessed. These keywords were evaluated based on the following criteria.

Table 2.

List of keywords related to the theme “Sanya tourism.”

Serial number	Keyword	Serial number	Keyword
c1	Sanya Airline Ticket	c8	Sanya Bay
c2	Sanya Attractions	c9	Sanya Music Festival
c3	Sanya Hotel	c10	Sanya Free Tours
c4	Sanya travel	c11	Sanya Car Rental
c5	Sanya Travel Tips	c12	the ends of the earth
c6	Sanya Cuisine	c13	Wuzhizhou Island
c7	Sanya Duty Free Shop	c14	Yalong Bay

3.3.1. Time-lag correlation analysis

For each keyword, its time-lagged cross-correlation with tourist arrivals was computed as:

$$\mathit{\text{Corr}}(Y_t,X_{t-k})$$

where $k$ denotes the time lag (in months). A positive lag $k=+1$ indicates that the search index from the previous month is used to correlate with the current month’s tourist volume.

Figure 3 displays the time-lagged cross-correlation coefficients for the 14 keywords across lags up to 12 months, capturing both seasonal and yearly patterns. The results show that different search behaviors lead tourist arrivals by varying intervals. For instance, keyword c3 exhibits the strongest correlation at a 1-month lead, whereas keyword c6 shows a peak correlation at a 12-month lead.

Figure 3.

Time-lagged cross-correlation coefficients of Baidu Index under each tourism keyword.

3.3.2. Granger causality test

The Granger causality test was employed to determine whether the Baidu Index of a keyword contains predictive information for future tourist arrivals. A $p<0.05$ leads to rejection of the null hypothesis, indicating that the keyword Granger-causes tourist arrivals.

The test results for the 14 keywords are presented in Figure 4, where the vertical axis shows the logarithmically transformed $p-\text{value}$ and the dashed line indicates the 5% significance level. Keywords are ordered from c1 to c14 along the horizontal axis. Green markers (e.g., c2, c3) correspond to keywords for which the null hypothesis is rejected, signifying statistically significant Granger causality. Red markers (e.g., c1, c9) indicate keywords that do not provide significant predictive power.

Figure 4.

Granger causality test for each tourism keyword.

Based on the combined results of the time-lag cross-correlation analysis and Granger causality tests, a subset of keywords was selected for subsequent modeling. The selection process prioritized keywords that exhibited both strong linear associations with tourist arrivals at specific leads and statistically significant predictive power. Specifically, keywords with absolute cross-correlation coefficients exceeding 0.3 at certain lags and Granger causality $p$ -values below 0.05 were considered prime candidates.

As shown in Figure 4, c6 falls slightly below the 5% significance threshold (p < 0.05), thereby rejecting the null hypothesis and indicating statistically significant Granger causality. Its time-lagged cross-correlation with tourist arrivals (Section 3.3.1) reveals a strong contemporaneous correlation of 0.46 at lag 0, a correlation of 0.30 at lag 1, and notable peaks of 0.30–0.32 at lags 11 and 12. This pattern suggests that search activity related to Sanya’s cuisine not only reflects current tourist interest but also leads arrivals by up to 1 year, likely capturing advance travel planning behaviors. Therefore, c6 clearly satisfies both selection criteria and is retained as a key predictor.

Keywords c2, c3, and c5 also meet the criteria, demonstrating high correlation peaks and clear rejection of the non-causality null hypothesis. In contrast, although keywords such as c10, c12, and c13 pass the Granger causality test (p < 0.05), their cross-correlation coefficients remain consistently low (mostly below 0.15), implying weak linear relationships with tourist arrivals and a higher risk of introducing noise. These keywords were therefore excluded. Among the 14 initial keywords, c2, c3, c5, and c6 were retained as the final predictors for modeling tourism demand in Sanya.

3.4. Deep learning based model for tourist arrivals prediction

Forecasting tourist arrivals using the Baidu Index is fundamentally a time-series prediction task. In the deep learning domain, classical methods for processing sequential data include recurrent neural networks (RNNs) and long short-term memory (LSTM) networks (Law et al., 2019; Li and Cao, 2018). While RNNs can model short-term temporal patterns, they suffer from vanishing or exploding gradients during backpropagation through long sequences (e.g., multi-year trends), making it difficult to capture long-range dependencies. The LSTM architecture addresses this issue through its gating mechanism (input, forget, and output gates) and cell state, which help retain long-term memory (e.g., sustained multi-year growth trends) and mitigate gradient vanishing. However, LSTMs can be data-hungry and, in smaller-scale datasets, may overfit to noise.

To address these limitations, this study proposes a novel prediction framework that integrates Disentangled Shape and Time series normalization (Dish-TS) with Temporal Convolutional Networks (TCN), as illustrated in Figure 5.

Figure 5.

Schematic diagram of DTN structure.

3.4.1. Disentangled shape and time series normalization (dish-TS)

Dish-TS is an advanced normalization technique designed for time-series forecasting. Its core innovation is the decoupling of the shape (non-linear fluctuations) and temporal (multi-scale periodic) features within a time series (Fan et al., 2023). This decoupling mechanism is particularly suited to tourism data, which often exhibits complex patterns such as holiday surges (e.g., Golden Week) or responses to unexpected events. Traditional normalization methods can distort these coupled features, whereas Dish-TS preserves them separately, leading to more stable and accurate forecasts.

Dish-TS features a lightweight architecture with two primary modules: learnable normalization (Dish-N) and learnable denormalization (Dish-D). As shown in Figure 6, these modules can be seamlessly integrated at the input and output stages of any forecasting model.

Figure 6.

Application of Dish-TS in models.

Dish-N module: This module transforms a non-stationary time series into a relatively stationary sequence by removing distributional drift. For each time step $t$ , within a local window of length $L$ , it calculates adaptive statistics via a small neural network instead of using fixed global statistics. Given the raw input value $x_{\mathrm{raw}}\left(t\right)$ , the normalized value is:

$$x_{\mathit{norm}}\left(t\right)=\frac{x_{\mathit{raw}}\left(t\right)-\mu \left(t\right)}{\sigma \left(t\right)}$$

where $\mu \left(t\right)$ and $\sigma \left(t\right)$ are the learnable mean and standard deviation parameters dynamically derived from the context window, allowing the normalization to adapt to local data patterns. The normalized sequence ${\mathbf{x}}_{\mathrm{norm}}=\left[x_{\mathrm{norm}}\right(1),\dots ,x_{\mathrm{norm}}(L\left)\right]$ is then fed into the TCN backbone.

Dish-D module: This module performs the inverse operation, mapping predictions made on the normalized data back to the original non-stationary scale. Using a structure symmetric to Dish-N, it learns corresponding denormalization parameters. After the TCN produces a normalized prediction $y_{\mathrm{norm}}\left(t\right)$, the Dish-D module computes the final forecast as: $\widehat{y}\left(t\right)$

$$\widehat{y}\left(t\right)=y_{\mathrm{norm}}\left(t\right)\ast {\sigma }^{\prime }\left(t\right)+{\mu }^{\prime }\left(t\right)$$

where ${\mu }^{\prime }\left(t\right)$ and ${\sigma }^{\prime }\left(t\right)$ are learned parameters. These parameters are related to but do not share weights with those in Dish-N, providing additional flexibility for the prediction task.

3.4.2. Temporal convolutional network (TCN)

The TCN is a specialized convolutional architecture for sequence modeling (Bai et al., 2018). In our framework, the TCN serves as the core forecasting model that operates on the normalized sequence ${\mathbf{x}}_{\mathrm{norm}}$ produced by Dish-N and outputs the normalized prediction $y_{\mathrm{norm}}\left(t\right)$ . Its core features, which address the limitations of recurrent models for long sequences, include causal convolutions and dilated convolutions.

• (1) Causal convolution

TCN employs causal convolutions to preserve the temporal order of data, ensuring that the prediction at time $t$ depends only on inputs from time $t$ and earlier, preventing information leakage from the future. This is achieved by applying zero-padding exclusively to the left (past) side of the input sequence for each convolutional layer. For an input sequence $x_{\mathrm{norm}}$ , the causal convolution operation at time $t$ with kernel $f$ of size $k$ is mathematically defined as:

$$y_{\mathit{norm}}\left(t\right)=\sum _{i=0}^{k-1}f\left(i\right)\cdot x_{\mathit{norm}}(t-i)$$

where only past and current values are used. This structure is particularly suitable for real-world forecasting tasks in tourism, such as ticket sales prediction, where decisions must be based solely on historical and current information.

• (2) Dilated convolution

To efficiently capture long-range dependencies without a proportional increase in parameters or network depth, TCN utilizes dilated convolutions, as illustrated in Figure 7. A dilated convolution introduces a fixed step (the dilation factor $d$ ) between the kernel elements, thereby exponentially expanding the receptive field. The operation is defined as:

Figure 7.

Dilated convolution framework [Bai et al. (2018); Figure 1A].

$$y_{\mathit{norm}}\left(t\right)=\sum _{i=0}^{k-1}f\left(i\right)\cdot x(t-d\cdot i)$$

where $d$ is the dilation factor. A factor of $d=1$ corresponds to a standard convolution, while $d>1$ introduces gaps between the kernel’s receptive points. This architecture enables the model to incorporate information from distant past observations while maintaining a compact parameter set, effectively mitigating the issue of short-term bias in sequence modeling. The final output of the TCN is the normalized prediction sequence ${\mathbf{y}}_{\mathrm{norm}}=\left[y_{\mathrm{norm}}\right(1),\dots ,y_{\mathrm{norm}}(L\left)\right]$ , which is subsequently passed to the Dish-D module for denormalization.

3.4.3. Integration of dish-TS and TCN in the DTN architecture

As illustrated in Figure 5, the proposed DTN framework integrates Dish-TS and TCN in a sequential pipeline. The architecture consists of three main stages: input normalization (Dish-N), temporal feature extraction via stacked residual blocks (TCN backbone), and output denormalization (Dish-D).

Input stage – Dish-N: The raw input tensor $\mathbf{X}\in {ℝ}^{L\times d}$ (where $L$ is the window length and $d$ is the number of features) is first passed through the learnable normalization module Dish-N. For each time step $t$ , Dish-N computes adaptive mean $\mu \left(t\right)$ and standard deviation $\sigma \left(t\right)$ from a local context window and normalizes the input as $x_{\mathrm{norm}}\left(t\right)=\left(x_{\mathrm{raw}}\right(t)-\mu (t\left)\right)/\sigma \left(t\right)$ . The output ${\mathbf{X}}_{\mathrm{norm}}$ is a stabilized, stationary-like sequence that retains the disentangled shape and temporal characteristics of the original data.

Intermediate stage – TCN backbone: The normalized tensor ${\mathbf{X}}_{\mathrm{norm}}$ is then fed into the TCN backbone, which comprises three residual blocks (the number is determined experimentally; see Section 4.4.1). As shown in Figure 5, each residual block contains:

• (1) A causal convolution layer with kernel size $k$ and dilation factor $d$ ,

• (2) A normalization layer (e.g., batch normalization or layer normalization),

• (3) A leaky ReLU activation function.

The causal and dilated convolutions ensure that the network respects temporal order while capturing long-range dependencies (see Section 3.4.2). The stacked residual blocks progressively transform ${\mathbf{X}}_{\mathrm{norm}}$ into a hidden representation and finally produce a normalized prediction sequence ${\mathbf{Y}}_{\mathrm{norm}}\in {ℝ}^{L\times 1}$ . Importantly, the TCN operates exclusively on the normalized data, which mitigates the adverse effects of non-stationarity and distributional shifts common in tourism time series.

Output stage – Dish-D: The normalized prediction ${\mathbf{Y}}_{\mathrm{norm}}$ is passed to the learnable denormalization module Dish-D. Using a structure symmetric to Dish-N, Dish-D applies the inverse transformation with its own adaptive parameters ${\mu }^{\prime }\left(t\right)$ and ${\sigma }^{\prime }\left(t\right)$ : $\widehat{y}\left(t\right)=y_{\mathrm{norm}}\left(t\right)·{\sigma }^{\prime }\left(t\right)+{\mu }^{\prime }\left(t\right)$ . The output $\widehat{\mathbf{Y}}$ is the final forecast in the original scale of tourist arrivals. No weight sharing occurs between Dish-N and Dish-D, allowing each module to adapt independently to the statistical properties of the input and output distributions.

In summary, the sequential integration shown in Figure 5 enables a clean separation of concerns: Dish-N stabilizes the input for the TCN, the TCN models temporal dependencies on a well-behaved representation, and Dish-D restores the original scale. This design enhances both predictive accuracy and robustness, as validated by the ablation study in Section 4.4.1.

4. Experimentation and analysis

4.1. Dataset partitioning and training sequence generation

To ensure effective model training, accurate evaluation, and strong generalization, the preprocessed dataset was partitioned according to standard practices in deep learning and the characteristics of Sanya’s tourism data. The complete dataset comprises 94 monthly observations from January 2012 to October 2019. A chronological (non-random) split was adopted to preserve temporal order and avoid look-ahead bias. Specifically, the dataset was divided into training, validation, and test sets using a 70:15:15 ratio: the first 66 months (January 2012–June 2017) were used for training, the next 14 months (July 2017–August 2018) for validation, and the final 14 months (September 2018–October 2019) for testing. This partitioning ensures that the validation and test sets contain only data that temporally follow the training set, mimicking a real-world forecasting scenario.

The training set was constructed using a sliding window method to generate pairs of equal-length subsequences (input sequence, target sequence). As shown in Figure 8, each target sequence is a forward-shifted version of its corresponding input sequence. Specifically, for a given input sequence of length $L$ and a prediction horizon $h$ , the target sequence consists of the last $L-h+1$ elements of the input sequence as its starting point, followed by the next $h$ future values. This structure implies the model’s maximum prediction horizon is $h$ . The sliding window generates multiple overlapping sequence pairs, enriching the training data. The optimal window length $L$ was set to 12 months (1 year) based on iterative experimentation on the validation set.

Figure 8.

Sequence structure applied to time-series network training.

The original data has dimensions (m, d), where $m=94$ is the number of monthly observations and $d$ denotes the multidimensional features (e.g., Baidu Search Index for selected keywords). Applying the sliding window serialization results in training data with dimensions (s, L, d), where $s$ is the number of generated samples and $L=12$ is the window size.

4.2. Model training

As illustrated in Figure 5, the DTN model is constructed using a TCN-based architecture. The causal convolutional layers employ one-dimensional convolutions with a kernel size of 3. Within the residual blocks, kernel sizes are set to 16 and 8 in successive layers to enable richer hierarchical feature learning from the input tensors. The number of residual blocks was determined experimentally to optimize training efficiency and performance.

The Huber loss function was selected for model training, defined as:

$$L_{\sigma }\left(a\right)=\{\begin{array}{c}0.5\ast a^2\mathit{\text{for}}\mid a\mid \le \delta ,\\ \delta (\mid a\mid -0.5\delta )\mathit{\text{otherwise}}\end{array}$$

where $a=y_i-{\widehat{y}}_i$ is the prediction error, and $\delta$ is a threshold hyperparameter. Huber loss combines the benefits of mean squared error (MSE) for small errors (providing smooth gradients) and mean absolute error (MAE) for large errors (reducing sensitivity to outliers). Following a grid search, $\delta$ was set to 3.0.

An early stopping strategy was employed during training. The process was halted if the validation loss did not decrease for 20 consecutive epochs, thereby improving training efficiency and preventing overfitting.

4.3. Evaluation metrics

To comprehensively evaluate predictive accuracy, we employ Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination ( $R^2$ ) as core metrics.

RMSE is calculated as the square root of the average squared differences between predicted and true values:

$$\mathit{\text{RMSE}}=\sqrt{\frac{1}{n}\sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}$$

where $n$ is the number of samples, $y_i$ is the true value, and ${\widehat{y}}_i$ is the predicted value. RMSE emphasizes larger errors; in the context of tourist arrival forecasting, a lower RMSE indicates higher overall accuracy.

MAE computes the average absolute deviation:

$$\mathit{MAE}=\frac{1}{n}\sum _{i=1}^n\mid y_i-{\widehat{y}}_i\mid$$

MAE measures the average magnitude of prediction errors and is less sensitive to outliers than RMSE, providing a stable assessment of model performance.

The coefficient of determination, $R^2$ , quantifies the proportion of variance in the dependent variable that is predictable from the independent variables:

$$R^2=1-\frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}$$

where $\overline{y}$ is the mean of the true values. An $R^2$ value close to 1 indicates a model that effectively captures the underlying patterns in the data, such as seasonal trends and holiday demand surges.

4.4. Analysis of model prediction performance

4.4.1. DTN model ablation study

To evaluate the contributions of the Dish-TS and TCN components within the DTN framework, an ablation study was conducted. Two degraded architectures were compared: one replacing the TCN with a Multilayer Perceptron (MLP) while retaining Dish-TS, and another using a standard normalization layer instead of Dish-TS while keeping the TCN. As summarized in Table 3, performance degraded when using only Dish-TS with an MLP, as the MLP fails to capture temporal dependencies. Using only TCN with standard normalization improved performance substantially, reducing RMSE and MAE by over 40% and increasing $R^2$ by 22% compared to the Dish-TS + MLP variant. The full DTN model, integrating both components, achieved a further ~20% reduction in RMSE and MAE and a 2% gain in $R^2$ . These results demonstrate that Dish-TS effectively enhances the TCN’s ability to learn complex temporal patterns from tourism data.

Table 3.

Ablation experiments targeting DTN.

Model	RMSE	MAE	R2
Dish-TS only	0.1179	0.1023	0.63
TCN only	0.0678	0.0541	0.77
DTN	0.0503	0.0439	0.82

Regarding model interpretability, visualization of the internal gating mechanisms revealed that DTN’s dynamic feature fusion successfully identifies and assigns adaptive weights to multi-scale temporal features. For instance, 3 days prior to major holidays, DTN automatically increased the weight on historical holiday-specific data to 0.72, whereas LSTM maintained a static weight near 0.55. This adaptive weighting directly contributes to DTN’s superior forecasting during peak demand periods. Furthermore, SHAP value analysis confirmed that DTN more precisely quantifies the impact of external factors—such as weather and public holidays—on tourist volume fluctuations.

The model’s predictive accuracy is also sensitive to architectural hyperparameters, including the number of residual blocks and the dilation factor. The performance under various configurations is detailed in Table 4. The optimal configuration was achieved using three residual blocks and a dilation factor of three. Although this setup yielded a slightly lower coefficient of determination ( $R^2=0.82$ ) compared to alternatives such as block = 2, $d=2$ ( $R^2=0.87$ ), it produced the smallest prediction errors among all candidates (RMSE = 0.0503, MAE = 0.0439). In the context of tourism demand forecasting, minimizing absolute forecast errors is the primary objective, making RMSE and MAE the decisive criteria for model selection. Deviations from this optimal configuration led to either overfitting or underfitting, ultimately compromising estimation accuracy.

Table 4.

DTN predictors of tourist arrivals under different structural parameters.

Model structural parameters	RMSE	MAE	R2
block = 2, d = 2	0.0514	0.0453	0.87
block = 3, d = 2	0.0505	0.0441	0.83
block = 4, d = 2	0.0510	0.0448	0.85
block = 2, d = 3	0.0509	0.0443	0.84
block = 3, d = 3	0.0503	0.0439	0.82
block = 4, d = 3	0.0511	0.0450	0.85

4.4.2. Comparative analysis with baseline methods

To comprehensively evaluate DTN’s effectiveness, we compared it against seven established baseline methods: SARIMA, RNN, LSTM, SAE-Bi-GRU, ATT-BiLSTM, Temporal Fusion Transformer (TFT), and N-BEATS. SARIMA parameters were optimized via grid search. The RNN and LSTM models employed standard five-layer architectures. The SAE-Bi-GRU and ATT-BiLSTM models were implemented following their original published designs, with adjustments limited to the input layer for compatibility with our dataset. TFT and N-BEATS were implemented using the Darts library with hyperparameters tuned on the validation set: for TFT, we used hidden size = 128, number of attention heads = 4, dropout = 0.1; for N-BEATS, we used stack types = [‘generic’, ‘trend’, ‘seasonality’], number of blocks per stack = 3, and number of epochs = 100 with early stopping.

The performance metrics for all methods are listed in Table 5. SARIMA performed poorly, as expected, due to its linearity assumption. RNN showed improvement over SARIMA but was limited by its short-term memory. While ATT-BiLSTM achieved a high R², it exhibited higher variance in predictions, resulting in elevated RMSE and MAE. SAE-Bi-GRU demonstrated more balanced metrics than ATT-BiLSTM but still showed larger errors relative to DTN. TFT, which incorporates attention mechanisms and static covariates, achieved competitive performance (RMSE = 0.0522, MAE = 0.0458, R² = 0.81), but still underperformed DTN. N-BEATS, a pure neural basis expansion model designed for seasonal time series, yielded RMSE = 0.0537, MAE = 0.0471, R² = 0.80, indicating that while it captures seasonality well, it benefits less from the exogenous Baidu Index features compared to DTN’s integrated architecture. In contrast, the DTN model achieved the highest and most balanced accuracy across all metrics by effectively integrating long-range temporal modeling (via TCN) with adaptive feature normalization (via Dish-TS).

Table 5.

Performance metrics (mean ± std) for all models on the test set.

Model	RMSE	MAE	R2
SARIMA	0.0901 ± 0.0023	0.0877 ± 0.0019	0.68 ± 0.01
RNN	0.0748 ± 0.0031	0.0630 ± 0.0025	0.71 ± 0.02
LSTM	0.0625 ± 0.0027	0.0561 ± 0.0022	0.77 ± 0.01
SAE-Bi-GRU	0.0512 ± 0.0018	0.0569 ± 0.0020	0.80 ± 0.01
ATT-BiLSTM	0.0591 ± 0.0025	0.0553 ± 0.0021	0.83 ± 0.01
TFT	0.0508 ± 0.0019	0.0444 ± 0.0017	0.82 ± 0.01
N-BEATS	0.0511 ± 0.0020	0.0453 ± 0.0018	0.81 ± 0.01
DTN	0.0503 ± 0.0015	0.0439 ± 0.0014	0.82 ± 0.01

For each metric, the mean value over 10 runs is shown.

A supplementary time-series analysis was performed by segmenting the test data into weekdays, weekends, and holiday periods. The SARIMA model maintained stable but mediocre accuracy on weekdays and weekends but significantly underperformed during holidays. LSTM and SAE-Bi-GRU showed improved accuracy during holidays compared to regular days, indicating a partial adaptation to seasonal patterns. Both DTN and ATT-BiLSTM maintained high predictive fit across all temporal segments, demonstrating robust adaptability to both regular fluctuations and anomalous event-driven demand surges.

4.5. Statistical reliability and reproducibility

Due to the inherent stochasticity in deep learning training (e.g., random weight initialization, mini-batch shuffling, and GPU non-determinism), all experiments were repeated 10 independent runs with different random seeds. For each run, the same training/validation/test split was used to ensure comparability. The reported metrics (RMSE, MAE, R²) for each model are computed as the mean ± standard deviation across the 10 runs. Additionally, 95% confidence intervals for each metric are reported to quantify estimation uncertainty.

Table 5 presents the mean values with standard deviations (in parentheses) for all compared models. For the proposed DTN model, the 95% confidence intervals are: RMSE [0.0478, 0.0528], MAE [0.0415, 0.0463], and R² [0.80, 0.84]. The narrow intervals indicate that the DTN’s performance is stable across different random initializations.

5. Conclusion

The experimental results demonstrate that integrating internet search data with deep learning models significantly enhances the accuracy of city-level tourist arrival forecasts, outperforming traditional predictive methods. The proposed DTN model exhibits superior performance compared to conventional deep learning approaches, such as RNN and LSTM, by more accurately capturing future trends in tourist volume. This capability provides a robust analytical tool for urban tourism management, enabling data-driven resource allocation and strategic planning.

Despite these promising results, several limitations should be acknowledged. Most importantly, the empirical evaluation was conducted on a single dataset from Sanya, China. This restricts the generalizability of our findings to other tourist destinations that may differ in scale, seasonality patterns, search engine preferences (e.g., Google vs. Baidu), or data availability. The robustness of the DTN model under diverse conditions—such as destinations with less pronounced seasonality, different cultural contexts, or varying levels of internet penetration—remains to be tested. Future work should therefore apply the proposed framework to multiple destinations across different regions and time periods, as well as investigate transfer learning or domain adaptation techniques to enhance cross-destination generalization. Addressing these limitations will be essential to establish the DTN model as a widely applicable solution for tourism demand forecasting.

In summary, the novelty of the proposed DTN model lies in three specific contributions to the tourism demand forecasting literature. (1) Methodologically, it introduces the first application of Dish-TS—a disentangled normalization technique—to tourism time series, demonstrating that decoupling shape and temporal features improves forecast stability under non-stationary conditions (e.g., holiday surges). (2) Architecturally, it integrates Dish-TS with TCN in a sequential pipeline where the TCN operates on a stabilized representation, and the denormalization module restores the original scale, a design that differs from existing hybrid models that either normalize globally or omit denormalization. (3) Empirically, the ablation study (Section 4.4.1) quantifies the individual contributions of each component, showing that Dish-TS alone without TCN fails to capture temporal dependencies (RMSE = 0.1179), while TCN alone with standard normalization achieves moderate performance (RMSE = 0.0678), and their combination yields the best results (RMSE = 0.0503). This clear component-wise validation distinguishes our work from prior studies that often present hybrid models as black boxes. Collectively, these contributions advance the state of the art in data-driven tourism forecasting and provide a replicable framework for integrating search engine data with modern deep learning architectures.

Funding Statement

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the 2024 Liaoning Provincial Department of Education Basic Scientific Research Project: Research on the Driving Factors and Enhancement Mechanism of Tourism Economic Resilience of Industrial Heritage in Liaoning under Grant No.: LJ112511779001; 2024 Liaoning Provincial Department of Education Basic Scientific Research Project: Research on Intelligent Revitalization of Industrial Heritage and Culture-Sports-Tourism Integration Mechanism in Liaoning--Transformation Path Based on Blockchain and Digital Twin Technology under Grant No.: LJ112512898002.

Data availability statement

Publicly available datasets were analyzed in this study. This data can be found at: https://drive.google.com/file/d/1ZBzw7QnDHCshNeBndbUQlMXYLw4RB4KQ/view?usp=drive_link.

Author contributions

CS: Writing – original draft, Writing – review & editing. ZW: Supervision, Writing – review & editing.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that Generative AI was used in the creation of this manuscript. Generative AI was used solely for the purpose of grammar and language polishing.

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