This study develops an easy forecasting model using prefectural data in Japan. The Markov chain known as a stochastic model corresponds to the vector auto-regressive (VAR) model of the first order. If the transition probability matrix can be appropriately estimated, the forecasting model using...

We propose a simple modification of the time series filter by Hamilton (2018b) that yields reliable and economically meaningful real-time output gap estimates. The original filter relies on 8-quarter ahead forecasts errors of an autoregression. While this approach yields a cyclical component of...

This paper investigates how the ordering of variables affects properties of the time-varying covariance matrix in the Cholesky multivariate stochastic volatility model. It establishes that systematically different dynamic restrictions are imposed when the ratio of volatilities is time-varying....

In this chapter, we first explain what we mean by a signal, and then we describe some characteristics such as energy, frequency, phase, power spectrum, etc. We show how to analyse it by the means of spectral analysis and Fourier transform. Moreover, as the Fourier transform does not provide any...