2004/04/01 by Peter C.B. Phillips, Peter C. B. Phillips, Katsumi Shimotsu · 1 citation
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Monetary Policy and Economic Impact #math.ST #msc:62M10. #stat.TH
paper · pdf · doi:10.1214/009053604000000139
published as Annals of Statistics 2004, Vol. 32, No. 2, 656-692
openalex publication_date 2004/04/01 · arxiv created 2004/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Asymptotic properties of the local Whittle estimator in the nonstationary case (d>½) are explored. For ½<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 polynomial trend of order α>½, the estimator is shown to be inconsistent and to converge in probability to unity.