Title: An exact expression for the Whittle approximation of the Gaussian likelihood and its application to parameter estimation
Authors: Suhasini Subbarao - Texas A&M (United States) [presenting]
Abstract: One important objective in time series analysis is to estimate the parameters of a conjectured time series model based on the observed time series. If the parameters in the model can be characterized in terms of their second order autocovariance structure, then there are two well-known methods for estimating the parameters; one in the time domain, the other in the frequency domain. The time domain approach is based on the (quasi) Gaussian likelihood, whereas in the frequency domain the Whittle likelihood is commonly used. The Whittle likelihood can be viewed as the Kullbach-Leibler distance between the periodogram and the conjectured spectral density. It is well known that the Whittle likelihood is an approximation of the Gaussian likelihood. We obtain an exact expression for this approximation in terms of biorthogonal random variables. This approximation can be used to obtain an alternative proof of Szego's theorem. We apply this approximation to the problem of parameter estimation, where we obtain a variant of the Whittle likelihood which has better finite sample properties.