Quasi-maximum exponential likelihood estimators for a double AR(p) model

Abstract

The paper studies the quasi-maximum exponential likelihood estimator (QMELE) for the double AR(p) (DAR(p)) model: yt = ∑i=1p φiyt-1 + ηt√w+∑i=1pα iy2t-i, where {ηt} is a white noise sequence. Under a fractional moment of yt with Eη2t < ∞, strong consistency and asymptotic normality of the global QMELE are established. A formal comparison is given with the QMLE in Ling (2007) and WLADE in Chan and Peng (2005). A simulation study is carried out to compare the performance of these estimators in finite samples. An example on the exchange rate is given.