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Articles 31 - 36 of 36
Full-Text Articles in Economics
Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Cowles Foundation Discussion Papers
This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d 0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a “plug-in” log-likelihood function that has the unknown mean replaced by the sample mean. The second …
Error Bounds And Asymptotic Expansions For Toeplitz Product Functionals Of Unbounded Spectra, Offer Lieberman, Peter C.B. Phillips
Error Bounds And Asymptotic Expansions For Toeplitz Product Functionals Of Unbounded Spectra, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper establishes error orders for integral limit approximations to traces of powers to the p th order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices are Fourier transforms of functions which we allow to be bounded, unbounded, or even to vanish on [- π,π ], thereby including important cases such as the spectral functions of fractional processes. Error rates are also given in the case in which the matrix product involves inverse matrices. The rates are sharp up to …
Local Whittle Estimation Of Fractional Integration, Katsumi Shimotsu, Peter C.B. Phillips
Local Whittle Estimation Of Fractional Integration, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter ( d ) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N (0,1/4) limit distribution for all values of d if the optimization covers an interval of width less than 9/2 and the initial value of the process is known.
Local Polynomial Whittle Estimation, Donald W.K. Andrews, Yixiao Sun
Local Polynomial Whittle Estimation, Donald W.K. Andrews, Yixiao Sun
Cowles Foundation Discussion Papers
The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent those problems. Instead of approximating the short-run component of the spectrum, φ(λ), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a “local polynomial Whittle” (LPW) estimator. Following the work of Robinson (1995a), we establish the asymptotic bias, variance, mean-squared error (MSE), …
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.