Modeling and forecasting of nonlinear nonstationary processes based on the Bayesian structural time series

The article describes an approach to modelling and forecasting non-linear non-stationary time series for various purposes using Bayesian structural series. concepts of non-linearity non-stationarity, as well methods processing non-linearity’sand non-stationarity in the construction models are considered. features nonlinearities nonstationaryare presented. An probabilistic-statistical based on has been studied. Parametric non-parametric include methods: classical autoregressive models, neural networks, support vector machines, hidden Markov models. Non-parametric state-space functional decomposition One types isBayesian main constructing Models process learning Bayesianstructural model is described. Training performed four stages: setting structure a priori probabilities; applying Kalman filter update state estimates observed data;application “spike-and-slab”method select variables model; averaging combine results make prediction. algorithm seriesmodel Various components BSTS considered andanalysed, with help which structures alternative predictive formed. As example application series, problem predicting Amazon stock prices base dataset amzn_share. After loading, data were analysed, missing values processed. characterized by irregular registration observations, leads large number “masking” possible seasonal fluctuations. This makes task rather difficult. To restore gaps amzn_sharetime linear interpolation method was used. Using set statistical tests (ADF, KPSS, PP), tested stationarity. divided into two parts: training testing. fitting filterand Monte Carlo according chain scheme. estimate simultaneously regularize regression coefficients, spike-and-slab applied. quality assessed.