Construction of Forecast Models based on Bayesian Structural Time Series

Abstract

The article discusses the methodology for solving problems of modeling and forecasting time series using the method of Bayesian structural time series (BSTS). The analysis used real stock price data from Amazon, Facebook, and Google over a period of three and a half years. The Bayesian model of the structural time series was described. The model is presented in the form of a state space. The learning process of the BSTS model is performed in four stages: setting the structural components of the model and a priori probabilities; applying a Kalman filter to update state estimates based on a set of input data; application of the "spike-and-slab" method to select variables in a structural model; averaging the results of the Bayesian model in order to make a forecast. An algorithm for constructing a BSTS model with predictors was developed. The process of fitting structural models of time series was performed using the Kalman filter and the Monte Carlo method according to the Markov chain scheme (MCMC). The results of modeling and forecasting of the BSTS model with predictors were compared with similar models without predictors. The calculation procedures and visualization were performed using the BSTS package implemented in R. The prediction accuracy for competing models was evaluated using prediction plots and a set of metrics: MAPE, MAE, RMSE, and Theil U statistics.