QUASI-MAXIMUM EXPONENTIAL LIKELIHOOD ESTIMATORS FOR A DOUBLE AR(p) MODEL

The paper studies the quasi-maximum exponential likelihood estimator (QMELE) for the double AR(p) (DAR(p)) model: y(t) = Sigma(p)(i=1)phi(i)y(t-i) + eta(t)root omega+Sigma(p)(t=1)alpha(i)y(t-i)(2), where {eta(t)} is a white noise sequence. Under a fractional moment of y(t) with E eta(2)(t) < infinity, 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.