Hybrid Time Series Forecasting with Limited Data: Combining Deep Learning and Traditional Models for Short- and Long-Term Prediction (http://doi.org/10.63386/617743)

Xiaorui Qian¹, Xiangpeng Zhan^1,* Guoshu Lai¹, Huawei Hong¹, Lingling Zhu², Kai Xiao¹, Ying Qu¹

¹State Grid Fujian Marketing Service Center (Metering Center), No. 264 Wusi Road, Gulou District, Fuzhou City, Fujian Province, China, Postcode 350003

²State Grid Fujian Electric Power Co., Ltd., No. 257 Wusi Road, Gulou District, Fuzhou City, Fujian Province, China, Postcode 350003

*Corresponding author: Xiangpeng Zhan

Email: 3022@mju.edu.cn

Xiaorui Qian Email: dannyqian1992@hotmail.com

Guoshu Lai Email: shixin@stu.mju.edu.cn

Huawei Hong Email: 2014302580081@whu.edu.cn

Lingling Zhu Email: huangqingyu@stu.mju.edu.cn

Kai Xiao Email: ziyangchen@stu.mju.edu.cn

Ying Qu Email: epquying@163.com

Funding

This work was supported by the Science and Technology Project of State Grid Corporation of China “Research on Key Technologies for Comprehensive Analysis, Forecast and Simulation, and Flexible Interaction of Electric Load Supporting the New Electricity System” (No. 5400-202455364A-3-1-DG)

Abstract

Time series forecasting is pivotal across domains such as finance, energy, healthcare, and supply chain management, yet it faces challenges due to the complex, dynamic, and non-linear nature of temporal data, particularly when historical data is limited. Traditional models like ARIMA, Exponential Smoothing, and Prophet excel in capturing trends and seasonality with modest data requirements, but struggle with complex non-linear dependencies. Conversely, transformer-based deep learning models effectively model intricate temporal relationships for short-term forecasting but require substantial data, underperforming in sparse or noisy conditions. This paper proposes a hybrid forecasting framework that integrates a transformer model for short-term predictions with the Prophet model for long-term trend and seasonality modeling, combining their outputs via an XGBoost regressor. Our approach enhances prediction accuracy by leveraging the complementary strengths of both models. We demonstrate superior performance over standalone models on benchmark datasets, particularly in data-constrained scenarios, and provide comprehensive evaluations to validate the framework’s effectiveness and generalizability.

Keywords: Pattern Recognition, Differential Privacy, Privacy Risk Auditing, Data Mining

1 Introduction

Time series forecasting [1 ] is critical across numerous domains, including finance [2], energy [3], healthcare [4 ], and supply chain management [5]. While accurate forecasting is essential for informed decision-making, it remains challenging due to the complex, dynamic, and often non-linear nature of temporal data. In many practical scenarios, particularly within industry and business applications, only limited historical data is available—typically ranging from several hundred to a few thousand observations. This constraint significantly influences the selection and performance of forecasting models.

Traditional statistical and machine learning approaches such as ARIMA [6], Expo- nential Smoothing [7], and more recently, Prophet [8], have demonstrated robust performance in forecasting tasks with relatively small datasets. These models excel at capturing trend and seasonality components, and their modest data requirements make them suitable for long-term forecasting in data-constrained environments. However, they often lack the flexibility to model complex, non-linear temporal dependencies.

Conversely, deep learning models, particularly transformer-based architectures [9– 11], have recently garnered attention in time series forecasting due to their capacity to model intricate temporal relationships and effectively handle multivariate sequences. Transformers are especially proficient at short-term forecasting where high-frequency patterns and contextual information are crucial. Nevertheless, these models typically require substantial volumes of data for effective training, and their performance can deteriorate when data is sparse or noisy—conditions frequently encountered in real- world applications.

To address these limitations, this paper proposes a hybrid time series forecast- ing framework that integrates the strengths of both deep learning and traditional models. Specifically, we employ a transformer-based model for short-term forecast- ing to capture high-resolution temporal dynamics, while utilizing the Prophet model

for long-term forecasting to leverage its robustness in modeling trend and seasonality with limited data. The outputs of these two models are subsequently integrated using an XGBoost regressor [12], which learns to optimally combine the short- and long- term forecasts. This hybrid approach aims to enhance overall prediction accuracy by capitalizing on the complementary strengths of each component model.

The contributions of this work are threefold:

We propose a novel hybrid forecasting architecture that integrates transformer and Prophet models via an XGBoost-based ensemble mechanism.
We empirically demonstrate that the hybrid model achieves superior performance compared to standalone models, particularly in scenarios with limited historical data.
We provide comprehensive evaluations on benchmark time series datasets to validate the effectiveness and generalizability of the proposed approach.

2 Related Work

Time series forecasting has received considerable attention across diverse domains, leading to the development of numerous models that tackle challenges such as trend identification, seasonality modeling, noise reduction, and data sparsity. Traditional statistical methods like Autoregressive Integrated Moving Average (ARIMA) [6] and Exponential Smoothing [7] have long been the go-to approaches for univariate fore- casting. These models are especially effective when data is limited, as they rely on relatively simple, interpretable assumptions and can model trend and seasonality with minimal data requirements. For long-term forecasting, these traditional methods are robust, particularly in scenarios where data is sparse or noisy. However, their perfor- mance declines when faced with complex, non-linear temporal relationships, which are common in real-world applications.

Machine learning models, such as Random Forests [13], Support Vector Regression (SVR) [14 ], and gradient boosting techniques like XGBoost [12], have gained pop- ularity due to their ability to capture non-linear dependencies and handle small to moderate datasets effectively. These models excel at long-term forecasting, especially when the temporal patterns are not highly intricate. However, they often struggle with short-term forecasting, particularly when high-frequency or fine-grained temporal pat- terns are crucial. Without the explicit incorporation of temporal features or advanced techniques to account for sequence dependencies, their performance can degrade for short-term predictions.

In contrast, deep learning models, particularly Recurrent Neural Networks (RNNs) [15], Long Short-Term Memory (LSTM) networks [16], and more recently, Transformer-based architectures [9–11], have demonstrated strong performance in short-term time series forecasting. These models excel at modeling complex temporal dynamics and long-range dependencies, often providing superior results for short-term predictions. Transformer models, in particular, have gained significant attention due to their self-attention mechanisms [17], which allow them to efficiently capture intri- cate, long-range dependencies across multivariate time series. However, deep learning

models typically require large volumes of data to effectively capture such dependen- cies. When data is sparse or noisy, deep learning models often suffer from overfitting or fail to generalize well, resulting in poor long-term forecasting performance.

Recent studies have proposed hybrid forecasting approaches that combine the strengths of both traditional statistical methods and deep learning techniques to address these limitations [18, 19]. These hybrid models decompose time series data into distinct components, such as trend, seasonality, and residuals, applying special- ized models to each component for improved accuracy. Additionally, ensemble learning techniques have been employed to combine predictions from different models, improv- ing robustness and predictive power. Despite these advancements, limited research has explicitly focused on hybridizing Transformer-based models with traditional mod- els like Prophet [8], particularly in data-constrained environments. Furthermore, the combination of deep learning models for short-term forecasting with statistical models for long-term forecasting, especially in low-resource settings, remains underexplored.

Our approach directly addresses these challenges by leveraging the strengths of both deep learning and machine learning models in a hybrid framework. Specifically, we combine a Transformer-based model for short-term forecasting, capitalizing on its ability to model high-frequency, complex temporal patterns, with Prophet for long- term forecasting, exploiting its robustness in trend and seasonality modeling when data is sparse. By integrating the outputs of these models through an XGBoost regressor, our approach aims to optimally combine short- and long-term forecasts, addressing the unique challenges posed by limited data availability and enhancing overall predictive accuracy.

3 Methodology

This section presents the architecture and training process of our proposed hybrid fore- casting model. The framework integrates a transformer-based deep learning model for short-term forecasting, a statistical model for long-term forecasting, and a tree-based ensemble learner to combine their predictions. The design leverages the complemen- tary strengths of each component and is especially effective in scenarios where only a limited number of historical observations (e.g., ~1000 data points) are available.

3.1 Short-Term Forecasting with Transformer

Transformer-based models are well known for their ability to capture complex tem- poral dependencies and nonlinear interactions within high-frequency signals. In this work, we adopt TimeXer [11], a variant of the canonical Transformer that is specif- ically designed to handle exogenous variables and temporal misalignments. Despite requiring relatively large datasets for optimal performance, we observe that TimeXer can perform competitively for short-term forecasting even on smaller datasets (with around 1000 records), provided that the prediction horizon is constrained to a small number of steps (e.g., 3–7 time steps). This is because short-term forecasting primar- ily relies on local temporal patterns and recent exogenous cues, both of which can be effectively learned from a limited context window.

Let x1:T denote the univariate target time series, and {z1(i:

covariate series. TimeXer proceeds as follows:

The endogenous series x1:T is segmented into non-overlapping patches of length P and embedded into a sequence of temporal tokens with position encoding.
A global token Gen is learned to aggregate contextual information across the entire series.
Each exogenous variable is embedded into a variate token using a linear projector, designed to accommodate temporal misalignments or irregularities.
Multi-head self-attention is applied to the endogenous tokens, while cross-attention from the global token to exogenous tokens allows contextual integration.
Thefinal representation is projected to produce short-term forecasts ˆ(y)T(s)1(r)t:T+Hs .

The short-term predictions are collected in a structured feature set for the hybrid model:

Fshort = {ˆ(y)t(short) | t = T + 1,…, T + Hs } .

3.2 Long-Term Forecasting with Prophet

Prophet [8] is a decomposable time series model that represents the signal as a sum of interpretable components:

y(t) = g(t) + s(t) + h(t) + ϵt ,

where g(t) captures trend, s(t) accounts for seasonality, h(t) models holiday or event effects, and ϵt represents noise. Due to its additive nature, Prophet is highly robust in settings with limited data, especially when the objective is long-term forecasting.

The strength of Prophet lies in its strong prior assumptions about time series structure. It can detect changepoints and fit logistic growth or piecewise linear trends, making it particularly suitable for datasets with ∼ 1000 observations and long forecasting horizons (e.g., 30–90 steps).

Prophet is independently trained on the same historical endogenous series x1:T , ignoring exogenous variables. The forecast output is:

For consistency, the horizon Hl can be aligned or made longer than Hs to evaluate both short- and long-term model integration.

3.3 Hybrid Forecasting via XGBoost Fusion

To effectively combine the strengths of both models, we train an XGBoost regressor to learn an optimal fusion strategy. XGBoost [12] is a gradient-boosted tree ensemble model known for its ability to handle small- to medium-sized datasets, robustness to overfitting, and automatic feature interaction discovery.

Before training XGBoost, wepreprocess the outputs from the short- and long-term models into feature vectors:

where metat includes timestamp-based covariates (e.g., day-of-week, hour-of- day, holiday indicator) or prediction uncertainties if available. These features are normalized and aligned to ensure compatibility across forecasting horizons.

The fusion model is then trained on a validation set with known ground truth values {yt } for t = T + 1,…, T + H by minimizing the squared loss:

XGBoost is a strong choice here for several reasons:

It efficiently models nonlinear relationships betweenmodel outputs and true values.
It supports missing values and works well with a small number of informative features.
It enables feature importance analysis, improving interpretability of the fusion process.

3.4 Practical Implementation of the Hybrid Model

Implementing the hybrid model in practice involves the following steps:

Data Preprocessing: Normalize the endogenous series, align exogenous variables (resample if necessary), and extract time-based features.
Model Training:

Train TimeXer on the endogenous and exogenous series for short-term prediction.
FitProphet to the endogenous series for long-term forecasting.

Output Alignment: Ensure that both models produce forecasts for a shared time window {T + 1,…, T + H}.
Feature Construction: Build fusion features ϕt from both model outputs and time-based metadata.
Fusion Training: Train an XGBoost model on validation data to minimize forecast error.
Inference: For new data, generate predictions using both base models, construct ϕt, and apply XGBoost to obtain the final forecast.

This hybrid framework can be efficiently deployed in production pipelines with minimal computational overhead. Each model component can be trained or updated independently, allowing for flexible retraining schedules tailored to the specific needs of the application (e.g., Prophet monthly, TimeXer weekly, XGBoost as needed). The modular architecture also supports extensions such as uncertainty estimation, dynamic reweighting of model outputs, and incorporation of additional models into the ensemble.

3.5 Hybrid Forecasting Algorithm

The algorithm encapsulates the essence of our hybrid approach: leveraging complemen- tary forecasting models and intelligently combining their outputs to produce a unified prediction that outperforms any individual component. By integrating the short-term pattern recognition capabilities of TimeXer with the robust long-term trend and sea- sonality modeling of Prophet, our framework addresses the fundamental challenge of accurate forecasting with limited historical data.

Algorithm 1 Hybrid Time Series Forecasting

Require: Endogenous series x1:T , Exogenous series {z1(i:

Ensure: Forecast y(ˆ)T+1:T+H

1: Train TimeXer on (x1:T , {z1(i:}) to get short-term forecast y(ˆ)short

2: Fit Prophet on x1:T to get long-term forecast y(ˆ)long

3: for t = T + 1 to T + H do

4: Extract features ϕt ← [ˆ(y)t(short) , ˆ(y)t(long) , metat]

5: Compute final forecast ˆ(y)t ← fXGB (ϕt )

6: end forreturn y(ˆ)T+1:T+H

4 Experiments and Evaluation

In this section, we empirically evaluate the proposed hybrid forecasting model across multiple real-world time series datasets. We aim to assess the effectiveness of our framework in both short-term and long-term forecasting tasks, particularly in low- resource settings with limited data availability.

4.1 Experimental Setup

4.1.1 Datasets

We conduct experiments on the following benchmark datasets, chosen for their diversity in temporal dynamics and practical relevance:

Electricity[20]: Hourly electricity demand data from regional power grids.
Traffic [21]:Hourly road occupancy rates across multiple sensors.
Weather[22]: Hourly meteorological data collected from global weather stations.
Retail [23]:Daily sales data for retail items across several categories.

All datasets are preprocessed to remove missing values and normalized to zero mean and unit variance. We use a rolling-window approach for train/validation/test splits, typically using 60% for training, 20% for validation, and 20% for testing.

4.1.2 Baselines

We compare our hybrid model against the following baselines:

Table 1 Short-Term Forecasting Performance (12-step horizon). Metrics are averaged over 5 datasets.

Model	Electricity	Traffic	Weather	Retail	Average MAE	Average RMSE
ARIMA	0.132	0.145	0.129	0.130	0.134	0.186
Prophet	0.126	0.132	0.124	0.129	0.128	0.179
LSTM	0.121	0.127	0.116	0.124	0.122	0.168
TimeXer	0.112	0.119	0.108	0.112	0.113	0.157
XGBoost	0.117	0.123	0.113	0.116	0.117	0.163
Hybrid (Ours)	0.104	0.111	0.099	0.106	0.105	0.146

ARIMA/SARIMA[6]: Classical statistical time series models.
Prophet[8]: Additive model for trend and seasonality.
XGBoost [12]:Tree-based regression with lag features.
LSTM [16]:Recurrent neural network for sequence modeling.
TimeXer [11]:Transformer-based model used standalone.
Hybrid(Ours): Our proposed model combining TimeXer, Prophet, and XGBoost.

4.1.3 Evaluation Metrics

We evaluate forecasting accuracy using three standard metrics:

All results are reported over the test set, averaged across multiple forecast horizons.

4.2 Performance Comparison

4.2.1 Short-Term Forecasting Results

Table 1 presents short-term forecasting performance (12-step horizon) across four benchmark datasets: Electricity, Traffic, Weather, and Retail. The hybrid model consistently outperforms all individual baselines in terms of MAE, RMSE, and MAPE, indicating its strong ability to capture both immediate patterns and under- lying temporal structure. In particular, the hybrid model improves over TimeXer and Prophet individually, validating their complementary roles—TimeXer capturing high-resolution dependencies, and Prophet modeling global trend and seasonality.

Figures 1, 2, 3, and 4 visualize model performance per dataset. Across all cases, the hybrid model shows the lowest error values and closely follows the ground truth trajectory, demonstrating improved predictive stability. The MAE/RMSE bar charts further highlight the advantage of combining models, and the forecast comparisons clearly reveal hybrid’s advantage over single-model alternatives.

4.2.2 Long-Term Forecasting Results

Table 2 reports long-term forecasting results using a 60-step horizon. Prophet per- forms reasonably well due to its explicit modeling of long-range trend and seasonality,

Table 2 Long-Term Forecasting Performance (60-step horizon). Metrics are averaged across 5 datasets.

Model	Electricity	Traffic	Weather	Retail	Average MAE	Average RMSE
ARIMA	0.225	0.236	0.215	0.221	0.219	0.282
Prophet	0.182	0.190	0.179	0.193	0.186	0.254
LSTM	0.191	0.198	0.189	0.194	0.193	0.266
TimeXer	0.203	0.211	0.198	0.191	0.201	0.273
XGBoost	0.184	0.191	0.183	0.193	0.188	0.259
Hybrid (Ours)	0.168	0.178	0.167	0.175	0.172	0.240

but the hybrid model consistently achieves the lowest errors across all datasets. The combination of TimeXer’s short-range pattern recognition and Prophet’s trend modeling—optimized by XGBoost—proves effective for long-term prediction.

In all datasets, as shown in Figures 1 to 4, the hybrid forecasts remain smooth yet reactive, with minimal drift compared to standalone models. This validates the robustness of the hybridization strategy across temporal scales.

(a) Forecast Comparison (b) TimeXer Attention Heatmap

Fig. 1 Evaluation results for the Electricity dataset.

(a) Forecast Comparison (b) TimeXer Attention Heatmap

Fig. 2 Evaluation results for the Traffic dataset.

4.3 Qualitative Analysis

The subfigures in Figures 1–4 provide further insights into the inner workings of the model:

Forecast Comparisons: These show that the hybrid model aligns closely with the ground truth across forecast windows, outperforming both TimeXer (which captures short-term but misses trend shifts) and Prophet (which models trends but lags behind dynamic shifts).
Attention Heatmaps: Self-attention maps from TimeXer reveal that the model emphasizes recent patches—explaining its effectiveness in short-term forecasting. The patch-level attention pattern demonstrates temporal localization that Prophet lacks.

4.4 Ablation Study

To quantify each component’s contribution, we conduct an ablation study (Table 3). For all datasets, removing TimeXer or Prophet significantly degrades performance, indicating that both components contribute unique value to the ensemble. Moreover, replacing XGBoost with a simple average ensemble yields inferior results—highlighting the importance of the fusion mechanism in learning optimal, nonlinear combinations

(a) Forecast Comparison (b) TimeXer Attention Heatmap

Fig. 3 Evaluation results for the Weather dataset.

Table 3 Ablation Study on Hybrid Model (MAE averaged across all datasets).

Model Variant	Electricity	Traffic	Weather	Retail	Avg MAE
Full Hybrid Model	0.104	0.111	0.099	0.106	0.105
w/o TimeXer (Prophet + XGBoost)	0.118	0.123	0.112	0.115	0.117
w/o Prophet (TimeXer + XGBoost)	0.115	0.121	0.107	0.110	0.113
w/o XGBoost (Avg. Ensemble)	0.111	0.118	0.108	0.108	0.111

of forecasts. These effects are clearly illustrated in the ablation plots for each dataset (Figures 1–4, subfigures (d)).

4.5 Robustness in Low-Resource and Missing Data Settings

Forecasting systems in real-world scenarios often operate under data scarcity or encounter missing records due to hardware failures or limited deployment histories. To simulate such conditions, we evaluate two robustness scenarios:

Missing Values: We randomly remove 20% of input values and impute them using simple strategies (forward fill or zeros).

(a) Forecast Comparison (b) TimeXer Attention Heatmap

Fig. 4 Evaluation results for the Retail dataset.

Table 4 Performance under Missing Data and Low-Resource Conditions (MAE shown).

Model	Electricity	Traffic	Weather	Retail	Missing Avg.	Low-Resource Avg.
Prophet	0.139	0.144	0.134	0.127	0.136	0.140
TimeXer	0.145	0.152	0.148	0.130	0.144	0.152
XGBoost	0.137	0.139	0.140	0.136	0.138	0.135
Hybrid (Ours)	0.120	0.122	0.118	0.114	0.121	0.118

Low-Resource Training: We restrict model training to the most recent 300–500 time steps, simulating early-stage deployment.

Table 4 presents the resulting MAE across datasets. While all models show perfor- mance degradation, the hybrid model remains significantly more accurate and stable than baselines. Prophet contributes robustness under small datasets, and XGBoost adapts well to sparse training regimes—ensuring reliable performance even under practical constraints.

These findings confirm that the proposed hybrid forecasting framework is not only accurate but also generalizable and robust to real-world challenges such as limited data and missing observations.

Table 5 Multivariate Forecasting Performance (average MAE per variable)

Model	Electricity Dataset	Weather Dataset
LSTM	0.123	0.134
TimeXer	0.110	0.120
XGBoost	0.116	0.128
Hybrid (Ours)	0.097	0.111

4.6 Extension to Multivariate Forecasting

Many time series forecasting tasks involve multiple interdependent variables (e.g., temperature, humidity, wind speed). To assess the adaptability of our method, we extend it to the multivariate setting.

In this case, each variable is treated as both a potential target and an exogenous input for others. For TimeXer, this aligns naturally with its design, as variate-wise attention can model inter-variable dependencies. For Prophet, forecasts are generated independently for each variable. The final hybrid output is obtained by training a separate XGBoost model per target variable using the combined short- and long-term predictions from other series.

We evaluate on the Weather and Electricity multivariate datasets. Table 5sum- marizesthe performance (averaged across all target variables). The hybrid model again demonstrates superior accuracy, benefitting from its ability to flexibly learn both intra- and inter-series dependencies.

These results highlight the generality and scalability of our method, which can handle both univariate and multivariate forecasting tasks under realistic conditions.

4.7 Discussion

Our results validate the hypothesis that combining models with complementary induc- tive biases leads to better forecasting performance. TimeXer captures fine-grained local dependencies, while Prophet models long-term trends with interpretable components. XGBoost effectively integrates their predictions with temporal metadata, adapting to both short- and long-range horizons. This combination proves particularly effective in low-data regimes, making it suitable for real-world forecasting deployments.

5 Conclusion and Future Work

This paper presents a hybrid time series forecasting framework that combines a transformer-based deep learning model (TimeXer), a statistical trend-seasonality model (Prophet), and a gradient-boosted decision tree regressor (XGBoost) to address the challenges of short- and long-term forecasting under limited data availability. The proposed architecture is motivated by the observation that deep learning models excel in capturing local and nonlinear patterns, while traditional models like Prophet offer robustness and interpretability for long-term trends, particularly in low-resource scenarios.

Through extensive experiments on real-world datasets—including electricity demand, traffic congestion, weather conditions, and retail sales—we demonstrate that

our hybrid model consistently outperforms strong baselines across various forecast- ing horizons. Detailed per-dataset analyses and visualizations confirm that the hybrid approach combines the strengths of its components, yielding both high accuracy and temporal stability.

We further show that the model maintains strong performance under missing data and limited training history, making it suitable for deployment in dynamic environ- ments with imperfect or evolving data streams. The ablation study reinforces the critical role of each component, particularly the XGBoost fusion layer, which learns to adaptively weight model outputs based on the temporal context.

Overall, the hybrid architecture provides a flexible, accurate, and robust solution to time series forecasting in practical, resource-constrained settings. Future work may extend this framework to multivariate and hierarchical forecasting tasks, incorporate uncertainty estimation, or explore adaptive fusion strategies for evolving time series domains.

While our hybrid forecasting framework demonstrates strong empirical perfor- mance, several avenues remain for future exploration. First, extending the model to multivariate and hierarchical forecasting scenarios could improve scalability for large- scale systems involving multiple interdependent time series. Second, incorporating probabilistic forecasting techniques or Bayesian ensembling could enhance uncertainty quantification, particularly for high-stakes applications. Third, adaptive fusion mech- anisms—such as attention-based or reinforcement-learned weighting of base model outputs—may improve robustness to distributional shifts and dynamic environments. Finally, deploying and evaluating the hybrid system in live production settings will provide valuable insights into its real-time performance, maintenance needs, and integration challenges.

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