A Methodology For Detecting Breaks In The Mean And Covariance Structure Of Time Series

Some structural break techniques defined in the time and frequency domains are presented to explore, at the same time, the empirical evidence of the mean and covariance instability by uncovering regime-shifts in some inflation series. To that effect, we pursue a methodology that combines two approaches; the first is defined in the time domain and is designed to detect mean-shifts, and the second is defined in the frequency domain and is adopted to study the instability problem of the covariance function of the series. The proposed methodology has a double interest since, besides the detection of regime-shifts occasioned in the covariance structure of the series, it allows taking into account the presence of mean-shifts in this series. Note that unlike the works existing in the literature which often adopt a single technique to study the break identification problem, our methodology combines two approaches, parametric and nonparametric, to examine this problem.