Backward Smoothing for Noisy Non-stationary Time Series

Abstract

In this study, we investigate a new smoothing approach to estimate the hidden states of random variables and to handle multiple noisy non-stationary time series data. Kunitomo and Sato (2021) have developed a new method to solve the smoothing problem of hidden random variables, and the resulting separating information maximum likelihood (SIML) method enables the handling of multivariate non-stationary time series. We continue to investigate the filtering problem. In particular, we propose the backward SIML smoothing method and the multi-step smoothing method to address the initial value issue. The resulting filtering methods can be interpreted in the time and frequency domains.