Estimating the differencing parameter via the partial autocorrelation function

This paper provides an explanation for the puzzling phenomenon in Tieslau et al. (1996, Journal of Econometrics 71, 249}264) that a substantial e$ciency loss occurs if low-order autocorrelations are omitted when estimating the di!erencing parameter, d. This is because for all n strictly bigger than 1, the nth-order autocorrelation function does not depend uniquely on the di!erencing parameter. We construct a new estimator for the di!erencing parameter based on the partial autocorrelation function. Comparisons of the asymptotic and "nite-sample variance of our estimator and those of TSB are made. A substantial e$ciency gain is achieved by our estimator as compared to TSB’s. ( 2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C22

[1]  Stanley E. Zin,et al.  Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates , 1993 .

[2]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[3]  Glenn D. Rudebusch,et al.  Long Memory and Persistence in Aggregate Output , 1989, Business Cycles.

[4]  F. Diebold,et al.  Real Exchange Rates under the Gold Standard , 1991, Journal of Political Economy.

[5]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[6]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[7]  Gary S. Shea,et al.  Uncertainty and implied variance bounds in long-memory models of the interest rate term structure , 1991 .

[8]  Richard T. Baillie,et al.  Analysing inflation by the fractionally integrated ARFIMA–GARCH model , 1996 .

[9]  Richard T. Baillie,et al.  Long memory processes and fractional integration in econometrics , 1996 .

[10]  Fallaw Sowell.  Maximum likelihood estimation of stationary univariate fractionally integrated time series models , 1992 .

[11]  A. I. McLeod,et al.  Fractional time series modelling , 1986 .

[12]  Peter Schmidt,et al.  A minimum distance estimator for long-memory processes , 1996 .

[13]  Ying-Wong Cheung,et al.  TESTS FOR FRACTIONAL INTEGRATION: A MONTE CARLO INVESTIGATION , 1993 .

[14]  Fallaw Sowell.  Modeling long-run behavior with the fractional ARIMA model , 1992 .

[15]  Tim Bollerslev,et al.  Cointegration, Fractional Cointegration, and Exchange Rate Dynamics , 1994 .

[16]  Philip Rothman,et al.  Fractional integration analysis of long-run behavior for US macroeconomic time series , 1994 .

[17]  Richard T. Baillie,et al.  Small sample bias in conditional sum-of-squares estimators of fractionally integrated ARMA models , 1993 .

[18]  Uwe Hassler,et al.  Long Memory in Inflation Rates: International Evidence , 1995 .

[19]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[20]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[21]  Bonnie K. Ray,et al.  ESTIMATION OF THE MEMORY PARAMETER FOR NONSTATIONARY OR NONINVERTIBLE FRACTIONALLY INTEGRATED PROCESSES , 1995 .

[22]  P. Phillips.  BOOTSTRAPPING I(1) DATA BY PETER C. B. PHILLIPS COWLES FOUNDATION PAPER NO. 1310 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS , 2010 .