Suhasini Subba Rao is a professor within the Department of Statistics at Texas A&M University. Subba Rao's research interests include time series, nonstationary processes, nonlinear processes, recursive online algorithms, spatio-temporal models. She did her PhD at the University of Bristol (under Prof. Bernard Silverman) and postdoctoral training at the University of Heidelberg (under Prof. Rainer Dahlhaus). Subba Rao has been at Texas A&M for almost 14 years, mainly working in time series analysis with applications to the geosciences (with an interest in climate change applications) and finance.
Talk: "Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain" (joint work with Junho Yang)
Zoom details will be provided via email announcements.
Abstract: In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussian likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to the discrete Fourier transform of the time series. Such a transformation yields a new decomposition for the inverse of a Toeplitz matrix and enables the representation of the Gaussian likelihood within the frequency domain. We show that the difference between the Gaussian and Whittle likelihood is due to the omission of the best linear predictions outside the domain of observation in the periodogram associated with the Whittle likelihood. Based on this result, we obtain an approximation for the difference between the Gaussian and Whittle likelihoods in terms of the best fitting, finite order autoregressive parameters. These approximations are used to define two new frequency domain quasi-likelihoods criteria. We show that these new criteria can yield a better approximation of the spectral divergence criterion, as compared to both the Gaussian and Whittle likelihoods. In simulations, we show that the proposed estimators have satisfactory finite sample properties.