Local Whittle estimation in nonstationary and unit root cases

By Peter C. B. Phillips, Katsumi Shimotsu. 2004

241 citations recorded by the source corpus.

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/108eaef0ccc1e2c832589107fc4a2837738345ea

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Citations in the corpus

A multivariate long-memory model with structural breaks (2009, methodology): “Semiparametric approaches are followed by Geweke and Porter-Hudak 28 , Robinson 29 , Velasco 30 , Phillips and Shimotsu 31 32 , and other.”
EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND (2009, unknown): “Gil-Alaña and Robinson (1997) applied Robinson’s (1994) LM test to macroeconomic data to test the null hypothesis that d = d0 for various values of d0, including d = 12 , and found that the results depend on how the short-run dynamics of the data is specified.”
Exact local Whittle estimation of fractionally cointegrated systems (2012, background): “Assumption 8 is also used in Phillips and Shimotsu (2004) in analyzing the asymptotics”
Exact Local Whittle Estimation of Fractional Integration (2005, unknown): “ymptotic theory for the LW estimator is discontinuous at d = 3 4 and again at d = 1, is awkward to use because of nonnormal limit theory and, worst of all, the estimator is inconsistent when d > 1 [8]. Thus, the LW estimator is not a good general-purpose estimator when the value of d may take on ”
Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration (2005, methodology): “The ranges of consistency and asymptotic normality for the LW estimator have been shown by Velasco ( 1999a ) and by Phillips and Shimotsu ( 2004 ) to be the same as those of the LPR estimator.”
LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION FOR NONLINEAR PROCESSES (2007, background): “Previous work by Robinson (1995b) and PS (2004) requires 1 m + m2β+1(logm)2 n2β → 0.”
Commodity futures and market efficiency (2013, methodology): “al Whittle estimator. The regression in Eq. 5 is then applied only for a part of the periodogram based on the same parameter mas for the local Whittle estimator1. 1In our analysis, we apply m = T0:6 (Phillips and Shimotsu, 2004). 6 3.2. Fractal dimension Contrary to the long-term memory, which can b”
Gaussian semiparametric estimation of multivariate fractionally integrated processes (2007, background): “Re h ( 0j) 1 Ij( 0 j ) 1 io a , ( 14 ) where ga is the ath row of (G0) 1 and {A}a denotes the ath column of matrix A.”
Unit root log periodogram regression (2007, background): “Similar consistency, inconsistency and boundary results apply to the LW estimator of d, as has been shown in Phillips and Shimotsu (2004).”