A1154
Title: Nonstationarity extended Whittle estimation of cyclical time series
Authors: Edward Hill - Queen Mary University of London (United Kingdom) [presenting]
Abstract: The Gegenbauer ARMA (GARMA) process is a fractional differencing model fitted to time series containing a strongly dependent cycle. In many real-world applications, the length of the cycle is unknown, and it is not clear whether the data is stationary. A definition of a GARMA process that also covers nonstationarity is provided. The model is characterised by the cyclicality parameter $\omega$, memory parameter $d$, and short memory AR and MA parameters. A two-stage procedure to estimate all the model parameters is provided. First, the cyclicality parameter $\omega$ is estimated by maximising the periodogram over the Fourier frequencies. The $n$-consistency and limit distribution of the estimator of $\omega$ are obtained. Next, the memory parameter $d$ and AR and MA parameters are estimated using a modified Whittle likelihood that uses the cycle frequency from the first stage estimator. The second stage estimates are shown to be consistent and asymptotically normal for both stationary and nonstationary GARMA processes. The complete estimation procedure allows for the construction of confidence intervals for all the GARMA model parameters, and Monte Carlo simulations confirm its good finite sample performance.
