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Full-Text Articles in Social and Behavioral Sciences
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 Bandwidth Selection In Heteroskedasticity-Autocorrelation Robust Testing, Yixiao Sun, Peter C.B. Phillips, Sainan Jin
Optimal Bandwidth Selection In Heteroskedasticity-Autocorrelation Robust Testing, Yixiao Sun, Peter C.B. Phillips, Sainan Jin
Cowles Foundation Discussion Papers
In time series regressions with nonparametrically autocorrelated errors, it is now standard empirical practice to use kernel-based robust standard errors that involve some smoothing function over the sample autocorrelations. The underlying smoothing parameter b, which can be defined as the ratio of the bandwidth (or truncation lag) to the sample size, is a tuning parameter that plays a key role in determining the asymptotic properties of the standard errors and associated semiparametric tests. Small- b asymptotics involve standard limit theory such as standard normal or chi-squared limits, whereas fixed-b asymptotics typically lead to nonstandard limit distributions involving Brownian bridge functionals. …