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In this book, we explain the development of a new filtering method to estimate the hidden states of random variables for multiple non-stationary time series data. This method is particularly helpful in analyzing small-sample non-stationary macro-economic time series. The method is based on the frequency-domain application of the separating information maximum likelihood (SIML) method, which was proposed by Kunitomo, Sato, and Kurisu (Springer, 2018) for financial high-frequency time series. We solve the filtering problem of hidden random variables of trend-cycle, seasonal, and...

This book presents a systematic explanation of the SIML (Separating Information Maximum Likelihood) method, a new approach to financial econometrics.
Considerable interest has been given to the estimation problem of integrated volatility and covariance by using high-frequency financial data. Although several new statistical estimation procedures have been proposed, each method has some desirable properties along with some shortcomings that call for improvement. For estimating integrated volatility, covariance, and the related statistics by using high-frequency financial data, the SIML...