Estimation of Fractional Integration in the Presence of Data Noise

A comparative study is presented regarding the performance of commonly used estimators of the fractional order of integration when data is contaminated by noise. In particular, measurement errors, additive outliers, temporary change outliers, and structural change outliers are addressed. It occurs that when the sample size is not too large, as is frequently the case for macroeconomic data, then non-persistent noise will generally bias the estimators of the memory parameter downwards. On the other hand, relatively more persistent noise like temporary change outliers and structural changes can have the opposite effect and thus bias the fractional parameter upwards. Surprisingly, with respect to the relative performance of the various estimators, the parametric conditional maximum likelihood estimator with modelling of the short run dynamics clearly outperforms the semiparametric estimators in the presence of noise that is not too persistent. However, when a non-zero mean is allowed for, it may reverse the conclusion.

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

[2]  Terence Tai-Leung Chong,et al.  Estimating the fractionally integrated process in the presence of measurement errors , 1999 .

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

[4]  Katsuto Tanaka,et al.  THE NONSTATIONARY FRACTIONAL UNIT ROOT , 1999, Econometric Theory.

[5]  Philip Hans Franses,et al.  The effects of additive outliers on tests for unit roots and cointegration , 1994 .

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

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

[8]  H. R. Kuensch.  Statistical Aspects of Self-Similar Processes , 1986 .

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

[10]  P. Robinson.  Gaussian Semiparametric Estimation of Long Range Dependence , 1995 .

[11]  P. Robinson.  Time Series with Long Memory , 2003 .

[12]  James Davidson,et al.  Modelling Political Popularity: an Analysis of Long‐range Dependence in Opinion Poll Series , 1997 .

[13]  Jan Beran,et al.  Maximum Likelihood Estimation of the Differencing Parameter for Invertible Short and Long Memory Autoregressive Integrated Moving Average Models , 1995 .

[14]  Lon-Mu Liu,et al.  Joint Estimation of Model Parameters and Outlier Effects in Time Series , 1993 .

[15]  Janet M. Box-Steffensmeier,et al.  The Dynamics of Aggregate Partisanship , 1996, American Political Science Review.

[16]  Domenico Marinucci,et al.  Alternative forms of fractional Brownian motion , 1998 .

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

[18]  Jesus Gonzalo,et al.  Long-range dependence in Spanish political opinion poll series , 2003 .

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

[20]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[21]  Philip Hans Franses,et al.  Long memory and level shifts: Re-analyzing inflation rates , 1999 .

[22]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[23]  P. Robinson.  Log-Periodogram Regression of Time Series with Long Range Dependence , 1995 .

[24]  Gawon Yoon.  Long-memory property of nonlinear transformations of break processes , 2005 .

[25]  P. Robinson,et al.  Testing of unit root and other nonstationary hypotheses in macroeconomic time series , 1996 .

[26]  Peter C. B. Phillips,et al.  Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes , 2002 .

[27]  Turalay Kenc,et al.  Ox: An Object-Oriented Matrix Language , 1997 .

[28]  Alex Maynard,et al.  Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly , 2001 .

[29]  C. Granger,et al.  Properties of Nonlinear Transformations of Fractionally Integrated Processes , 2000 .

[30]  C. Granger,et al.  Varieties of long memory models , 1996 .

[31]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

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

[33]  William R. Parke.  What is Fractional Integration? , 1999, Review of Economics and Statistics.

[34]  P. Phillips,et al.  Local Whittle estimation in nonstationary and unit root cases , 2004, math/0406462.

[35]  Peter C. B. Phillips,et al.  Log Periodogram Regression: The Nonstationary Case , 2006 .

[36]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[37]  F. Breidt,et al.  The detection and estimation of long memory in stochastic volatility , 1998 .

[38]  Niels Haldrup,et al.  Measurement Errors and Outliers in Seasonal Unit Root Testing , 2000 .

[39]  P. Robinson.  Long memory time series , 2003 .