Abstract:
In nonparametric Bayesian time series analysis, Whittle’s likelihood provides a well-established method to model a stationary time series. In general, Whittle’s likelihood constitutes an approximation to the true likelihood. It often yields asymptotically correct inference results, however at the price of losses in efficiency. Recently, Whittle’s likelihood was generalized [1] by first fitting any suitable parametric model (beyond Gaussian white noise) in the time domain and then applying a nonparametric correction in the frequency domain. This yields a pseudo likelihood that inherits the correct second order structure from the nonparametric spectral correction as well as the dependence between periodogram ordinates from the parametric fit. We present an extension of this approach to multivariate time series and give an outlook to upcoming tasks and challenges
