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The paper describes the use of Bayesian regression for building time seriesmodels and stacking different predictive models for time series. Using Bayesianregression for time series modeling with nonlinear trend was analyzed. Thisapproach makes it possible to estimate an uncertainty of time series predictionand calculate value at risk characteristics. A hierarchical model for timeseries using Bayesian regression has been considered. In this approach, one setof parameters is the same for all data samples, other parameters can bedifferent for different groups of data samples. Such an approach allows usingthis 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. Inthe study of predictive models stacking, the models ARIMA, Neural Network,Random Forest, Extra Tree were used for the prediction on the first level ofmodel ensemble. On the second level, time series predictions of these models onthe validation set were used for stacking by Bayesian regression. This approachgives distributions for regression coefficients of these models. It makes itpossible to estimate the uncertainty contributed by each model to stackingresult. The information about these distributions allows us to select anoptimal set of stacking models, taking into account the domain knowledge. Theprobabilistic approach for stacking predictive models allows us to make riskassessment for the predictions that are important in a decision-making process.

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