Title: Spectral analysis of Markov switching GARCH models
Authors: Maddalena Cavicchioli - University of Modena and Reggio Emilia - Dipartimento di Economia Marco Biagi (Italy) [presenting]
Abstract: Matrix expressions in closed form are derived for the autocovariance function and the spectral density of Markov switching GARCH models and their powers. For this, we apply the Riesz-Fischer theorem which defines the spectral representation as to the Fourier transform of the autocovariance function. Under suitable assumptions, we prove that the sample estimator of the spectral density is consistent and asymptotically normally distributed. Further statistical implications in terms of order identification and parameter estimation are discussed. These methods are well suited for financial market applications, and in particular for the analysis of time series in the frequency domain, as shown in the proposed numerical and real-world examples.