Bayesian Regression Approach for Building and Stacking Predictive Models in Time Series Analytics (2201.02034v1)

Abstract: The paper describes the use of Bayesian regression for building time series models and stacking different predictive models for time series. Using Bayesian regression for time series modeling with nonlinear trend was analyzed. This approach makes it possible to estimate an uncertainty of time series prediction and calculate value at risk characteristics. A hierarchical model for time series using Bayesian regression has been considered. In this approach, one set of parameters is the same for all data samples, other parameters can be different for different groups of data samples. Such an approach allows using this model in the case of short historical data for specified time series, e.g. in the case of new stores or new products in the sales prediction problem. In the study of predictive models stacking, the models ARIMA, Neural Network, Random Forest, Extra Tree were used for the prediction on the first level of model ensemble. On the second level, time series predictions of these models on the validation set were used for stacking by Bayesian regression. This approach gives distributions for regression coefficients of these models. It makes it possible to estimate the uncertainty contributed by each model to stacking result. The information about these distributions allows us to select an optimal set of stacking models, taking into account the domain knowledge. The probabilistic approach for stacking predictive models allows us to make risk assessment for the predictions that are important in a decision-making process.

• The paper details a Bayesian regression approach that builds standalone and ensemble models for time series forecasting by quantifying model parameter uncertainty.
• It demonstrates how Bayesian methods outperform traditional OLS by effectively modeling nonlinear trends and assessing prediction risks, including value-at-risk.
• The study implements a two-level model stacking technique using base learners like ARIMA and Neural Networks to improve forecast reliability in applications such as sales forecasting.

Bayesian Regression Approach for Building and Stacking Predictive Models in Time Series Analytics

In "Bayesian Regression Approach for Building and Stacking Predictive Models in Time Series Analytics," Bohdan M. Pavlyshenko details an effective probabilistic modeling technique aimed at enhancing the predictive performance for time series data. This paper provides a thorough examination of using Bayesian regression to build standalone time series models and to construct ensembles via model stacking, with a particular focus on applications to sales forecasting.

Central to this paper is the application of Bayesian regression in modeling time series data, including those with nonlinear trends—a significant departure from conventional OLS methods where uncertainty resides in the data. Bayesian regression introduces parameter uncertainty which is particularly advantageous when data is limited. Notably, this method enables the estimation of a posterior distribution of the model parameters, offering an insight into prediction uncertainty and allowing the calculation of value-at-risk (VaR).

The paper explores hierarchical Bayesian models that cater to different levels of data granularity. In such models, both shared and group-specific parameters are considered, facilitating efficient use of models even when historical data is scarce. This capability is demonstrated in the context of sales forecasting where new products or stores lack extensive data histories.

For model stacking, a two-level ensemble approach is employed where initial predictions from ARIMA, Neural Networks, Random Forest, and Extra Trees models form the base level. These predictions serve as covariates for a Bayesian regression at the ensemble's second level. This framework allows for an evaluation of model-specific uncertainty contributions via a probabilistic characterization of stacking regression coefficients, leading to informed model selection based on domain knowledge.

Empirical analysis included data from the "Rossmann Store Sales" dataset, illustrating the robust performance of Bayesian regression methods. Strong numerical results emphasize the model's adept handling of uncertainty and highlight its utility in risk assessment, particularly in decision-making processes where model reliability and risk quantification are cruical.

Beyond practical applications, theoretical implications include an enhanced understanding of model performance dynamics in conditions of limited data. Exploring various configurations of prior distributions for regression coefficients demonstrates potential avenues for further convergence upon optimal predictive outcomes, with informative prior distributions serving as a conduit for expert knowledge infusion into the modeling process.

Speculatively, this research paves the way for future advancements in AI-driven predictive analytics by leveraging Bayesian approaches in ensemble methods. As the field progresses, integrating Bayesian frameworks may become increasingly valuable for devising robust, uncertainty-aware predictive solutions in a range of complex, data-scarce scenarios across domains beyond sales forecasting. Enabling informed decision-making through quantifiable uncertainty measures marks an important evolution in advanced analytics strategies.