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A Complete Asymptotic Series For The Autocovariance Function Of A Long Memory Process, Offer Lieberman, Peter C.B. Phillips
A Complete Asymptotic Series For The Autocovariance Function Of A Long Memory Process, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d in (-1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,q) model. The leading term of the expansion is of the order O (1/ k 1-2 d ), where k is the autocovariance order, consistent with the well known power law decay for such processes, and is shown to be accurate to an error of O(1/ k 3-2d ). The derivation uses Erdélyi’s (1956) expansion for Fourier-type integrals when there are critical points …
Optimal Estimation Of Cointegrated Systems With Irrelevant Instruments, Peter C.B. Phillips
Optimal Estimation Of Cointegrated Systems With Irrelevant Instruments, Peter C.B. Phillips
Cowles Foundation Discussion Papers
It has been know since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such “irrelevant” deterministic trend instruments may be systematically used to produce asymptotically efficient estimates of a cointegrated system. The approach is convenient in practice, involves only linear instrumental variables estimation, and is a straightforward one step procedure with no loss of degrees of freedom in estimation. Simulations reveal that the procedure works well in practice, having little finite sample bias …