Exact Local Whittle Estimation of Fractional Integration

By Katsumi Shimotsu, Peter C. B. Phillips. 2005

143 citations recorded by the source corpus.

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 applies throughout the stationary and nonstationary regions of d and which 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.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2416d03cbb7f36b346a81491874b5583feba20ec

Citations in the corpus

• Simple (but effective) tests of long memory versus structural breaks (2006, unknown): “As shown by Shimotsu and Phillips (2005), the exact local Whittle estimator is consistent and asymptotically N (0, 1/4) for d 0 ∈ (∆ 1 , ∆ 2 ) if ∆ 2 − ∆ 1 ≤ 9/2 and µ 0 = 0.”
• Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach (2007, unknown): “(8) Concentrating Qm(d,G) with respect to G, Shimotsu and Phillips (2005) define the ELW estimator as d̂a = arg min d∈[∆1,∆2] Ra (d) , (9) where Ra (d) = log Ĝaa (d)− 2d 1 m mX j=1 log λj , Ĝaa (d) = 1 m mX j=1 I∆dxa (λj) , and −∞ ∆1 ∆2 ∞ are the lower and upper bounds of the admissible…”
• Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration (2005, unknown): “An exact local Whittle (ELW) estimator has been proposed by Shimotsu and Phillips ( 2005 ) that avoids some of the approximations in the derivation of the LW estimator and is valid for any value of d .”
• Fully modified narrow‐band least squares estimation of weak fractional cointegration (2011, unknown): “…but at a slower rate than T to remain 3Note that we could alternatively write our Assumptions 1-4 in terms of the model (5) and the errors vt, as in e.g. Shimotsu & Phillips (2005). in a neighborhood of the origin, where we have assumed some knowledge of the form of the spectral density.”
• Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting (2006, unknown): “recently extended and refined by Lobato (1999) and Shimotsu & Phillips (2002) among others.”
• Log Periodogram Regression: The Nonstationary Case (2006, unknown): “An asymptotic theory for this estimator has not been developed, but the approach is entirely analogous to the exact local Whittle (ELW) estimator studied in Shimotsu and Phillips (2005).”
• Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes (2003, unknown): “…approximation can be applied to nonstationary fractional component models and used to adapt the methods which have been suggested elsewhere (e.g., Phillips, 1999, Shimotsu and Phillips, 2001) for estimating the memory parameter in such models to cases where there are fractional components.”
• Refined Inference on Long Memory in Realized Volatility (2008, unknown): “Other semiparametric procedures include the local Whittle estimator (Künsch, 1987; Robinson, 1995b) and the exact local Whittle estimator (Shimotsu and Phillips, 2005), which is consistent for all values of d .”
• EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND (2009, unknown): “X1 is an acceptable estimator of μ0 for large d0; 3. for d0 ∈ [ 1 2 , 3 4 ] , both X and X1 are acceptable estimators of μ0.”
• Nonparametric cointegration analysis of fractional systems with unknown integration orders (2010, unknown): “, Phillips & Ouliaris (1988), Stock & Watson (1988), and Shintani (2001), in the same way that the univariate variance ratio statistic is related to, e.”
• Exact local Whittle estimation of fractionally cointegrated systems (2012, unknown): “the following approximation by Lemma 5.8 of Shimotsu and Phillips (2005) is relevant: Jn(ei j) = log j + (i/2)( j) + O( 2 j) + O(j 1 ).”
• Local Whittle estimation in nonstationary and unit root cases (2004, unknown): “This estimator has recently been shown by the authors [ Shimotsu and Phillips (2002) ] to be consistent and to have the same N(0, 14) limit distribution for all values of d. While it is still too early for”