A0348
Title: Whittle estimation of strongly dependent time series with random cycles
Authors: Edward Hill - Queen Mary University of London (United Kingdom) [presenting]
Liudas Giraitis - Queen Mary University of London (United Kingdom)
Abstract: A two-stage estimation procedure for the parameters of a second-order stationary time series containing a random cycle is described. The autoregressive cyclically integrated moving average (ARCIMA) process is a new fractional differencing model that captures both persistence and periodicity in data. In this framework, the cyclicality of the process is first estimated by maximizing the periodogram over the Fourier frequencies. Plugging in this estimated cycle frequency into a Whittle likelihood function, estimates of the remaining parameters of the ARCIMA model, specifically the autoregressive and moving average coefficients and also the fractional differencing parameter, can be obtained. It is shown that the Whittle estimates of these parameters are $\sqrt{n}$-consistent and asymptotically normal. Simulations suggest good performance of the two-stage procedure.
