M.I. Zernov, A.A. Sizov

Model and method are proposed for multiple time series analysis and prediction to improve forecasts in case of conditional heteroskedasticity, noise and nonstationarity. The proposed multiple time series model differs in multicomponent structure of trend and residuum obtained by fuzzy transform that makes it possible to reveal and increase interdependency of variables hidden in a multivariate process and ensures stability in case of conditionally heteroskedastic data. The proposed method consist in extraction of trend in every one-dimensional time series with the help of fuzzy transform and trend forecasting by the use of multivariate quantile regression with quantile adjustment. The value of residuum is analyzed and forecasted separately in case of necessity. The method consists of the following basic stages: multiple time series analysis; noise attenuation and trend extraction; forecasting system adjustment; time series forecasting; forecasting system adaptation. Thus the proposed method differs from existing methods in multistep procedure of fuzzy transform that obtain trends and in the following forecasting by the use of multivariate quantile regression that makes it possible to improve forecasts in case of noise and nonstationarity of data. As provided by research into efficiency of the proposed method forecast precision is improved by twenty percents in average in comparison with classical regression methods. In addition trend obtained by fuzzy transform proved to be smoother than the one after classical methods of smoothing like exponential smoothing and moving average method. Correlation between one-dimensional time series that form a multiple time series becomes considerably stronger.