The Empirical Properties of Some Popular Estimators of Long Memory Processes

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, H, or the fractional integration parameter, d, in long memory time series. We compare and contrast their performance on simulated Fractional Gaussian Noises and fractionally integrated series with lengths between 100 and 10,000 data points and H values between 0.55 and 0.90 or d values between 0.05 and 0.40. We apply all 12 estimators to the Campito Mountain data and estimate the accuracy of their estimates using the Beran goodness of t test for long memory time series.

[1]  Murad S. Taqqu,et al.  Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator , 1997 .

[2]  L. Oxley,et al.  Estimators for Long Range Dependence: An Empirical Study , 2009, 0901.0762.

[3]  On the integral of the squared periodogram , 2000 .

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

[5]  Patrice Abry,et al.  Wavelet Analysis of Long-Range-Dependent Traffic , 1998, IEEE Trans. Inf. Theory.

[6]  Patrice Abry,et al.  A Wavelet-Based Joint Estimator of the Parameters of Long-Range Dependence , 1999, IEEE Trans. Inf. Theory.

[7]  A. Walden,et al.  Wavelet Analysis and Synthesis of Stationary Long-Memory Processes , 1996 .

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

[9]  J. Beran.  A Goodness‐Of‐Fit Test for Time Series with Long Range Dependence , 1992 .

[10]  R. Baillie,et al.  Modeling and forecasting from trend-stationary long memory models with applications to climatology , 2002 .

[11]  R. Dahlhaus.  Efficient parameter estimation for self-similar processes , 1989, math/0607078.

[12]  R. Bhattacharya,et al.  THE HURST EFFECT UNDER TRENDS , 1983 .

[13]  T. Higuchi.  Approach to an irregular time series on the basis of the fractal theory , 1988 .

[14]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[15]  W. Palma.  Long-Memory Time Series: Theory and Methods , 2007 .

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

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

[18]  Murad S. Taqqu,et al.  Theory and applications of long-range dependence , 2003 .

[19]  B. Mandelbrot.  Limit theorems on the self-normalized range for weakly and strongly dependent processes , 1975 .

[20]  Jong-Suk Ruth Lee,et al.  Comparison of various estimators in simulated FGN , 2007, Simul. Model. Pract. Theory.

[21]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[22]  P. Robinson.  Semiparametric Analysis of Long-Memory Time Series , 1994 .

[23]  A. Raftery,et al.  Space-time modeling with long-memory dependence: assessing Ireland's wind-power resource. Technical report , 1987 .

[24]  Mark J. Jensen.  Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter , 1997 .

[25]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Ignacio N. Lobato,et al.  Averaged periodogram estimation of long memory , 1996 .

[27]  M. Taqqu,et al.  Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series , 1986 .

[28]  Clive W. J. Granger,et al.  An introduction to long-memory time series models and fractional differencing , 2001 .

[29]  Lajos Horváth,et al.  LIMIT THEOREMS FOR QUADRATIC FORMS WITH APPLICATIONS TO WHITTLE'S ESTIMATE , 1999 .

[30]  Patrice Abry,et al.  Long‐range Dependence: Revisiting Aggregation with Wavelets , 1998 .

[31]  P. Robinson,et al.  Variance-type estimation of long memory , 1999 .