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Modified Local Whittle Estimation Of The Memory Parameter In The Nonstationary Case, Katsumi Shimotsu, Peter C.B. Phillips
Modified Local Whittle Estimation Of The Memory Parameter In The Nonstationary Case, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of …
Local Whittle Estimation In Nonstationary And Unit Root Cases, Katsumi Shimotsu, Peter C.B. Phillips
Local Whittle Estimation In Nonstationary And Unit Root Cases, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d . For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.