(Bi)spectral analysis of Markov switching bilinear time series

We derive matrix expressions in closed form for the higher-order moments, the autocovariance function and the spectral and bispectral densities of Markov switching bilinear models and their powers. Under suitable assumptions, we prove that the sample estimators of the spectral and bispectral density matrices are consistent and asymptotically normally distributed. A simulation study confirms the validity of the asymptotic properties. These methods are also well suited for the analysis of time series in the frequency domain, as shown in some proposed real-world examples.