Enhancing Predictive Accuracy with Hybrid Statistical–Deep Learning Models for Multivariate Time Series Forecasting: A Systematic Review with Taxonomy and Decision Framework

4.4. Computational Trade-offs (Latency, Cost, Memory)

To evaluate forecasting accuracy, practical deployment of hybrid statistical–deep learning models also depends on computational requirements. Hybrid models generally achieve improved predictive performance by combining statistical stability with deep learning flexibility; however, this improvement often involves higher training complexity, memory consumption, and computational costs. Therefore, model selection should consider the balance between forecasting accuracy and operational feasibility (Table 3).

Table 3. Computational and deployment trade-offs of forecasting models.

This analysis highlights that hybrid models are most suitable for large, complex, and nonlinear forecasting problems, whereas simpler approaches may remain preferable for applications requiring low latency and limited computational resources.

4.5. Forecast Horizon–Based Performance Differences

The reviewed studies demonstrated that forecasting performance varied considerably across short- term, medium- term, and long-term horizons. The analysis indicated that forecasting horizon influenced error propagation, model stability, and the ability of different architectures to capture temporal dependencies. Short-term forecasting studies generally achieved strong performance using statistical and lightweight hybrid approaches because of lower uncertainty and limited dependency requirements. Medium-term forecasting applications benefited from hybrid models that effectively combined statistical trend extraction with deep learning-based residual learning. In contrast, long-term forecasting tasks demonstrated greater reliance on advanced deep learning and decomposition-based hybrid architectures due to their ability to capture complex and long-range temporal relationships (Table 4).

Table 4. Forecast horizon-based performance comparison of hybrid models.

A comparative synthesis was conducted by examining forecasting horizon, dataset quality, baseline adequacy, experimental fairness, and statistical rigor across the selected studies. The assessment indicated variation in methodological strength among reviewed studies, with some studies providing stronger evidence through transparent datasets, comprehensive baseline comparisons, robust validation procedures, and advanced statistical evaluation (Table 5).

Table 5. Evidence quality assessment of reviewed studies.

4.6. Dataset Characteristics and their Impact

The suitability of the datasets used has a significant effect on the performance of the hybrid models. Some of the common attributes that influence the predictive power of hybrid models are stationarity, dimensionality and noise.

4.6.1. Stationarity

Stationarity is a set of statistical characteristics of a time series being unchanged with time, including the mean and the variance. Hybrid models, especially those which incorporates statistical elements such as ARIMA are more suitable with stationary time series whereby the underlying patterns do not shift radically with time. Nevertheless, when non-stationary data are considered, deep learning models, in particular LSTM, can be especially useful, as a lack of stationarity is not assumed, and they are able to extract patterns in data that change with time.

4.6.2. Dimensionality

Multivariate time series can include many variables, which may have a major impact on the model. The hybrid models, including VAR-LSTM and SARIMA-GRU, are especially useful when dealing with high-dimensional data as they consist of the benefits of statistical models in addressing inter-variable correlation with the potential of deep learning models to work with large volumes of input data. As it was shown by [50], hybrid models trained on high-dimensional data sets (i.e. energy consumption data with a high number of influencing factors) always performed better than univariate or even multivariate models.

4.6.3. Noise

Noise in time series data is the random variation which is not based on the underlying patterns. The hybrid models are also most useful when dealing with noisy data since the deep learning techniques can learn a large set of data and determine trends that statistical approaches may fail to detect.

The analysis of hybrid models’ performance across data regimes is discussed in Table 6 below.

Table 6. Hybrid model performance across data regimes.

4.7. Failure-Mode Analysis of Hybrid Models

In this review, hybrid models are often heralded for their ability to improve forecasting accuracy. However, in certain contexts, hybrid models fail to outperform simpler statistical models or deep learning methods. Failure-mode analysis reveals several situations where hybridization may not be beneficial.

4.7.1. Overfitting

Hybrid models that include deep learning components, such as LSTM or GRU, may overfit when training data is limited, leading to poor generalization. This issue is particularly evident in domains like financial forecasting, where volatility and noise can cause LSTM-based hybrids to memorize noise rather than capture meaningful patterns.

4.7.2. Increased Computational Complexity

In cases where the dataset is low-dimensional, hybrid models involving complex deep learning layers (e.g., LSTM or CNN) may increase computational costs without offering a corresponding improvement in accuracy. For example, in short-term forecasting applications where ARIMA alone suffices, hybridization may lead to unnecessary complexity and longer training times.

4.7.3. Poor Performance in Noisy Data

Hybrid models, especially those that integrate statistical methods with deep learning, may fail to improve accuracy in highly noisy environments. The additional deep learning layer may struggle to filter out noise effectively, leading to minimal performance improvements compared to pure statistical models.

4.7.4. Non-Improvement in Short-Horizon Forecasting

When the forecast horizon is short-term, deep learning models often struggle to provide significant improvements over traditional statistical models, which can capture immediate temporal dependencies more effectively. For example, ARIMA models frequently outperform hybrid models for short-term forecasts in stable, low-dimensional datasets.

4.8. Computational and Practical Considerations

Although hybrid models have an important advance in terms of accuracy, there are also some computation and practical issues that have to be resolved. These are training cost, model interpretability and feasibility of deployment.

4.8.1. Training Cost

Hybrid models, particularly models with deep learning elements may be computationally costly to train. Deep learning model training, be it LSTM or GRU, takes a large number of computational resources and time, particularly in the case of large datasets. Such models as LSTM-ARIMA hybrids may need hours or even days of training time based on the size of the dataset. This is unlike the traditional statistical models which are usually very fast and less computationally intensive. Nevertheless, hybrid models tend to have more advantages in terms of accuracy than the increased training costs depending on the complexity of the task of forecasting, and in situations where the quality of prediction is the most important criteria.

4.8.2. Interpretability

Deep learning models are powerful models with a high probability of lacking interpretability, and it is challenging to know how the model is arriving at the predictions. This is a crucial problem in areas like finance and healthcare where decision-making processes of the predictions should be known to the stakeholders. Thus, it is possible to find a compromise between the precision of deep learning and the explainability of statistical tools in the hybrid models.

4.8.3. Deployment Feasibility

Hybrid models may be difficult to deploy in real-life applications because the models are more complex and require more computation. Nevertheless, hybrid models can be implemented in real-time decision-support systems. The added complexity of the hybrid models is warranted in such applications by the enhancement in the forecasting accuracy. Also, hybrid models enjoy the support of developments in cloud computing and distributed processing that can be used to alleviate the difficulties of deploying the models through scalable and efficient execution of the model.

Table 7 below summarises the properties of datasets and computation of some of the selected hybrid models surveyed.

Table 7. Dataset characteristics and their impact on hybrid models.

5. DISCUSSION

5.1. Key Insights from the Review

The synthesis comprised core statistical–deep learning hybrid studies together with a limited set of explicitly identified contextual benchmark studies. Conclusions concerning hybrid architecture, integration mechanisms, and forecasting gains were based primarily on the core hybrid evidence, while comparative and graph-based benchmark studies were used only to contextualise baseline performance, cross-variable modelling capability, computational trade-offs, and conditions under which hybridisation may not be necessary.

The high performance of hybrid models is attributed to the fact that they are able to identify both the linear and non-linear dependencies. ARIMA and VAR are good statistical models for modelling linear trends, seasonality, and stationarity in time series data, as was shown in research by [6, 20]. Deep learning models, including LSTM or GRU, on the other hand, are better at capturing non-linear dependence and long-term dependence that are often missing in statistical models. All these complementary strengths are taken advantage of by these hybrid models, and hence they are very versatile and can produce more accurate predictions. Indicatively, [24] established that hybrid systems such as ARIMA to capture linear and LSTM to refine non-linear forecasts of financial time series yielded better financial time series forecasting accuracy than non-hybrid ARIMA and LSTM regression systems.

ARIMA-LSTM and SARIMA-GRU stand out as some of the most prevalent architectures to work with since it gives a solid framework for addressing both short-term dynamics and intricate non-linear interactions. As an example, Liu et al., [20] observe that this hybrid combination is effective in energy forecasting, in which ARIMA models deal with the linear tendency, and LSTM networks address the sophisticated temporal relationships that arise in the residues. Lei et al., [22] also focus on the prevalence of graph-based hybrid models such as METRO (GNN), which use temporal-spatial graphs to predict multivariate time series in the domains of traffic and energy. Such architectures are also being strongly favoured due to the fact that they are more suited to support the interdependency between two or more time series variables, which is a common feature of real-world applications.

5.2. Statistical Interpretability vs Deep Learning Flexibility

One of the main themes that can be identified in the review is a trade-off between statistical interpretability and flexibility of deep learning. It is a generally accepted opinion that statistical models are more transparent and interpretable. To illustrate, ARIMA models are founded on mathematical concepts that have known principles, and their coefficients can be interpreted in most cases to explain how past values affect future predictions. Such an interpretable level is essential in such research areas as finance and healthcare, where interested parties require comprehending the logic of forecasts. According to [17], this transparency is a considerable benefit of statistical models, particularly when the regulatory or decision-making authorities demand an unambiguous answer to the way to get a particular forecast. Deep learning models, including LSTM and GRU, on the contrary, allow more flexibility in the modelling of complex patterns, particularly non-stationary, high-dimensional data [24]. This flexibility, however, comes with the trade-off of interpretability. The deep learning models are usually referred to as black-box models since it is a hard task to follow how certain inputs can produce certain outputs. This non-transparency is a major challenge to the explainability of what the model predicts, particularly in areas such as healthcare, where interpretation of model decisions is a key element in terms of trust and safety.

The hybrid strategy tries to find a compromise between these conflicting requirements. Hybrid models provide an avenue to higher accuracy and, at the same time, exhibit some degree of interpretability by providing the statistical rigour of the ARIMA or SARIMA models with the flexibility of the deep learning models. According to Mishra et al., [7], deep learning models alone might be more accurate in their predictions compared to the conventional approach, but the hybrid variant provides a more intuitive approach with no performance loss.

Nevertheless, explainability is still an issue even in hybrid models. As emphasised by Zhao et al., [46] the hybrid model can lead to superior results; however, it does not necessarily make the deep learning aspect more interpretable. The interpretability offered by the statistical model of a hybrid approach is accompanied by the fact that the deep learning aspect is always complicated, and there is still a need to develop explainable AI (XAI) methods to ensure that such models can be trusted and implemented in sensitive matters.

5.3. Performance Mechanisms and Variation Across Hybrid Models

The reviewed studies indicated that hybrid statistical–deep learning models improved forecasting performance by combining complementary modelling capabilities. Statistical components reduced forecasting bias by capturing linear trends, seasonality, and historical dependencies, while deep learning components improved nonlinear pattern recognition and residual error correction. These advantages were particularly evident in high-dimensional datasets, noisy environments, and forecasting problems involving complex nonlinear relationships.

However, differences in reported performance occurred due to variations in dataset characteristics, baseline model selection, forecasting horizons, and validation strategies. Models demonstrated stronger improvements when evaluated on large, complex datasets with appropriate benchmark comparisons, whereas simpler datasets or weaker validation approaches produced less consistent results. Therefore, hybrid model effectiveness depended not only on architecture selection but also on the characteristics and requirements of the forecasting problem.

5.4. Methodological Limitations in Existing Studies

Although the outcomes of the studies reviewed are promising, the methodological limitations which complicate the generalizability and the strength of findings are quite a few. The use of small datasets is one of the greatest problems. Numerous studies, especially those in small domains such as healthcare forecasting or environmental prediction, use small datasets, which might not fully address the variability of the real-world phenomenon that it seeks to model. A point raised by Khosravi et al., [6] was the possibility of overfitting in hybrid models due to inadequate data, because a model may work well on the training data but fail to effectively generalise to novel and unexplored data. This weakness underscores the significance of larger and more heterogeneous datasets to test hybrid models, particularly when using applications such as energy forecasting or financial prediction, where data is more likely to be richer and more fluid.

The other major concern is the fact that benchmarking in studies is not consistent. Although most of the studies use RMSE and MAE as measures of evaluation, there is not much consistency in the selection of the baseline models with the aim of comparison. He et al., [24] highlighted that the comparison of hybrid models to pure statistical or pure deep learning models is not necessarily justified and standardised when it comes to the choice of baselines. This lack of consistency complicates arriving at conclusive findings on the effectiveness of the hybrid models in various fields.

In addition, many of the hybrid model papers do not involve ablation studies, and thus it is impossible to determine the contribution of each component of the hybrid model to overall performance. Mishra et al., [7] observe that hybrid models are likely to perform better than standalone models, although the role of the deep learning component compared to the statistical component cannot be established without ablation studies. The execution of such studies would assist in drawing clarity on the contribution of various elements of a hybrid model to accuracy gains and assist practitioners to choose the appropriate combination of elements in their particular forecasting assignment.

5.5. Implications for Machine Learning and Statistics

Hybrid modelling is a transmission of traditional models to state-of-the-art machine learning techniques, providing a new approach to the problems of making predictions based on multivariate time series. Because statistical methods like ARIMA or VAR can be used to combine with deep learning models, like LSTM or CNN, such hybrid systems are useful in modelling both linear and non-linear relationships in the data. This integration greatly increases the prediction power of time series forecasting models and provides a wide range of application potential in different fields, such as finance, energy, health and environmental care [50].

Hybrid models can be important to explainable AI (XAI), exposing deep learning approaches to a greater level of interpretability. Although deep learning models are frequently criticised because of being black-box models, hybrid models that integrate statistical methods provide an avenue through which predictions can be explained. ARIMA models would, as an example, be able to give an understanding of the trend and seasonality of the data, which can be complemented by the deep learning model, which can represent intricate non-linear trends. This may be used to address the discrepancy between accuracy and explainability, which is a critical factor in such a domain as healthcare, where it is vital to understand the transparency of AI decisions used. In addition, hybrid models stand at the right spot to deal with numerous real-life issues in predictive applications.

5.6. Open Challenges and Future Research Directions

Hybrid forecasting techniques that combine both statistical and deep learning techniques have proven highly effective in enhancing predictive accuracy on Multivariate Time Series (MTS). Nevertheless, with the field’s development, several unresolved issues are still open, and they may influence the trend of future research. The scalability of hybrid models to high-dimensional multivariate time series is one of the leading challenges. The so-called curse of dimensionality is the exponential increase in computational cost and data demands as the size of the feature set or time series variables is enlarged. Financial and other energy prediction Data of high dimensionality can result in models that are computationally expensive and overfitted. High-dimensional data applications such as stock market prediction or environmental observing. Various methods that could be investigated in the future to address these difficulties include Principal Component Analysis (PCA), autoencoders, or sparse learning to enable hybrid models to be more effective in large-scale, high-dimensional applications.

The explainability and model transparency of hybrid models, especially those that include deep learning elements such as the LSTM or GRU, is also another important challenge. Although these models may provide high predictive power, they are usually black-box models, in which the reasons that are used to make the predictions are hard to decipher. Such interpretability has been a major challenge in other areas like healthcare, where knowing how AI has made decisions is fundamental to user trust and clinical implementation. Transformers with attention has become a major trend in time series forecasting, especially since 2022. Transformers were initially created as a Natural Language Processing (NLP) application, having been shown to be capable of modelling long-range dependencies and long-range complex temporal patterns in sequential data. Future studies are supposed to investigate the ways that these Transformer-based architectures can be extended with custom statistical models in order to improve their capabilities of handling large and complex-sized datasets and thus progress the state of the art in long-term forecasting.

Finally, the attempt to create automated hybrid model selection by means of AutoML (Automated Machine Learning) and Bayesian optimisation methods can be considered as one of the most promising research directions in the future. AutoML systems could potentially automate the procedure of choosing optimal model architectures and hyperparameters for a particular task, drastically decreasing the amount of time and experience one needs to build a model. Further evolution of these methodologies will make the hybrid forecasting models more flexible and accessible and be able to apply to larger and more complex datasets, making the predictions of these models more transparent, interpretable, and optimised. Finally, the concerns of scalability, explainability, transformer integration, and automated model selection will provide new opportunities for hybrid models to achieve substantial improvements in time series forecasting in the broad scope of domains.

5.7. Future Research Directions

Future research should address several methodological gaps identified in the reviewed literature. First, greater attention is required toward uncertainty-aware hybrid forecasting, as many existing studies focus only on point prediction without providing prediction intervals or confidence estimation. Second, external validation remains limited, with many models evaluated only on specific datasets or single application domains, restricting generalisability. Third, improved reproducibility is needed through transparent reporting of datasets, model parameters, and publicly available implementations. Fourth, future studies should incorporate deployment benchmarking by evaluating computational cost, inference speed, memory requirements, and scalability. Finally, the development of adaptive hybrid models for streaming data environments is needed to address concept drift, continuous learning requirements, and real-time forecasting challenges.

CONCLUSION

This is a systematic literature review that summarises the current developments in hybrid statistical-deep learning models of multivariate time series forecasting. The main results indicate the great benefits of hybrid models in enhancing the accuracy of forecasting in several fields, such as finance, energy, health, and environmental monitoring. Recent hybrid models, that is, models based on a mixture of statistical algorithms such as ARIMA, SARIMA and VAR and deep learning algorithms such as LSTM, GRU, and CNN, leverage the advantages of both paradigms in an attempt to resolve the complexities of multivariate time series data. All of these models provide a good tradeoff between being linear and non-linear, providing an opportunity to capture short-term dependency and long-range temporal relationships in a much better way than single models.

Using the reviews of 44 studies, it is easy to find that hybrid models are always better than either pure statistical models or pure deep learning models. In particular, it was common to find that ARIMA-LSTM and SARIMA-GRU hybrids performed well in terms of modelling linear trends and seasonality, whereas deep learning elements performed well in terms of modelling non-linear dependencies and long-term effects. Not only does the addition of predictive power from multivariate time series models contribute, but the contribution of this review also has some value to the increasingly growing research in the area of statistics-driven Machine Learning (ML). Using classical statistical models and contemporary deep learning models, this work draws attention to the possibility of hybrid models serving as an intermediary between the two spheres. Overall, hybrid forecasting models can be considered as a potent and adaptable means of multivariate time series forecasting. They provide major advancements in predictive accuracy, strength, and extrapolation in different fields. Nevertheless, issues still exist, especially in scalability, interpretability and efficiency of the models, which have to be tackled in future studies. The area of hybrid models can only improve as deep learning continues to develop and as transformer-based architectures and automated model selection tools such as AutoML are integrated, which should further improve the performance and accessibility of hybrid models. In this review, the future of hybrid models has been highlighted as promising and can potentially bring a revolution in the field of forecasting in multifaceted, high-dimensional areas.