  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.
