Title: Multiple local Whittle estimation of long memory
Authors: Josu Arteche - University of the Basque Country UPV/EHU (Spain) [presenting]
Abstract: The estimation of the memory parameter in long memory series has attracted great attention from the last few years of the 20th century onwards. Most research has focused on standard long memory at frequency zero, where several semiparametric estimators have been proposed for stationary, non-stationary and non-invertible series. However, much less attention has been paid to the existence of seasonal or cyclical strong persistence, where several spectral poles can appear at non-zero frequencies. In fact, the existing proposals only cover the stationary and invertible case. Based on the Exact Local Whittle estimation for standard long memory, we propose a semiparametric estimation technique for jointly estimating all the memory parameters in seasonal and cyclical long memory time series. Consistency and asymptotic normality are proved for stationary, non-stationary and non-invertible series, allowing for straightforward standard inference of interesting hypotheses such as the existence of unit roots at some or all seasonal frequencies. The fine finite sample performance of our procedure is analysed via Monte Carlo.