A1260
Title: Nonstationarity and cyclicality extended Whittle estimation
Authors: Edward Hill - Queen Mary University of London (United Kingdom) [presenting]
Abstract: The estimation of a time series exhibiting a persistent cycle is considered. Such dynamics are common in economic, epidemiological and geophysical data and encompass stationary cyclical long memory, nonstationary cyclical dependence and cyclical unit-root behaviour. The generalised Gegenbauer autoregressive moving average (GARMA) process provides a flexible framework for modelling this wide class of oscillatory phenomena. Using a modified Whittle likelihood function based on a corrected periodogram, the parameter estimates of the GARMA model are shown to be consistent and asymptotically normal in both stationary and nonstationary settings. In addition, the asymptotic properties of the estimator are unaffected by preliminary estimation of the cycle frequency. Monte Carlo simulations confirm the good finite-sample performance of the procedure and an application to United Kingdom influenza infections data illustrates its practical usefulness for modelling persistent seasonal dynamics.
