Frequency Regression and Smoothing for Noisy Nonstationary Time Series

Abstract

We develop a new regression method called frequency regression and smoothing. This method is based on the separating information maximum likelihood developed by Kunitomo and Sato (2021) and Sato and Kunitomo (2020) for estimating the hidden states of random variables and handling noisy nonstationary (small sample) time series data. Many economic time series include not only the trend-cycle, seasonal, and measurement error components, but also factors such as structural breaks, abrupt changes, trading-day effects, and institutional changes. Frequency regression and smoothing can be applied to handle such factors in nonstationary time series. The proposed method is simple and applicable to several problems when analyzing nonstationary economic time series and handling seasonal adjustments. An illustrative empirical analysis of the macroconsumption in Japan is provided.