Estimators of long-memory: Fourier versus wavelets

Journal of Econometrics

Volumn 151, Issue 2, 2009, Pages 159-177

  Faÿ, Gilles ^a   Moulines, Eric ^b   Roueff, François ^b   Taqqu, Murad S ^c  

^a UNIVERSITÉ LILLE 1   (France)

^b INSTITUT TELECOM   (France)

^c Boston University   (United States)

Author keywords

Long range dependence; Semi parametric estimation; Wavelet analysis

Indexed keywords

FOURIER; FOURIER METHODS; LOCAL REGRESSION; LOCAL WHITTLE; LONG RANGE DEPENDENCE; LONG-MEMORY; ON-DEMAND; RELATIVE STRENGTH; SEMI-PARAMETRIC ESTIMATION; SIMULATION-BASED;

FOURIER TRANSFORMS; TIME SERIES; WAVELET ANALYSIS; WAVELET TRANSFORMS;

ESTIMATION;

EID: 67650745188     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2009.03.005     Document Type: Article

References (60)

1. Abadir K., Distaso W., and Giraitis L. Nonstationarity-extended local whittle estimation. J. Econom. 141 (2007) 1353-1384
2. Abry P., Flandrin P., Taqqu M.S., and Veitch D. Wavelets for the analysis, estimation and synthesis of scaling data. In: Park K., and Willinger W. (Eds). Self-Similar Network Traffic and Performance Evaluation (2000), Wiley (Interscience Division), New York 39-88
3. Abry P., Flandrin P., Taqqu M.S., and Veitch D. Self-similarity and long-range dependence through the wavelet lens. In: Doukhan P., Oppenheim G., and Taqqu M.S. (Eds). Theory and Applications of Long-range Dependence (2003), Birkhäuser 527-556
4. Abry P., and Veitch D. Wavelet analysis of long-range-dependent traffic. IEEE Trans. Inform. Theory 44 1 (1998) 2-15
5. Andrews D.W.K., and Guggenberger P. A bias-reduced log-periodogram regression estimator for the long-memory parameter. Econometrica 71 2 (2003) 675-712
6. Andrews D.W.K., and Sun Y. Adaptive local polynomial Whittle estimation of long-range dependence. Econometrica 72 2 (2004) 569-614
7. Bardet J.-M. Testing for the presence of self-similarity of Gaussian time series having stationary increments. J. Time Ser. Anal. 21 (2000) 497-515
8. Bardet J.-M. Statistical study of the wavelet analysis of fractional Brownian motion. IEEE Trans. Inform. Theory 48 4 (2002) 991-999
9. Bardet J.-M., Lang G., Moulines E., and Soulier P. Wavelet estimator of long-range dependent processes. 19th Rencontres Franco-Belges de Statisticiens (Marseille, 1998). Stat. Inference Stoch. Process. 3 1-2 (2000) 85-99
10. Cohen A. Numerical Analysis of Wavelet Methods. Studies in Mathematics and its Applications vol. 32 (2003), North-Holland Publishing Co., Amsterdam
11. Dalla V., Giraitis L., and Hidalgo J. Consistent estimation of the memory parameter for nonlinear time series. J. Time Ser. Anal. 27 2 (2006) 211-251
12. Daubechies I. Ten lectures on wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics vol. 61 (1992), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
13. Deo R., Hsieh M., Hurvich C.M., and Soulier P. Long memory in nonlinear processes. Dependence in Probability and Statistics. Lecture Notes in Statist. vol. 187 (2006), Springer, New York 221-244
14. Deo R., Hurvich C.M., and Lu Y. Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment. J. Econom. 131 1-2 (2006) 29-58
15. Faÿ G., Moulines E., and Soulier P. Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes. Statist. Probab. Lett. 66 3 (2004) 275-288
16. Faÿ G., Roueff F., and Soulier P. Estimation of the memory parameter of the infinite-source Poisson process. Bernoulli 13 2 (2007) 473-491
17. Fox R., and Taqqu M.S. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 2 (1986) 517-532
18. Geweke J., and Porter-Hudak S. The estimation and application of long memory time series models. J. Time Ser. Anal. 4 (1983) 221-238
19. Giraitis L., Robinson P.M., and Samarov A. Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long range dependence. J. Time Ser. Anal. 18 (1997) 49-61
20. Granger C.W.J., and Joyeux R. An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1 1 (1980) 15-29
21. Hannan E.J., and Nicholls D.F. The estimation of the prediction error variance. J. Amer. Statist. Assoc. 72 360, part 1 (1977) 834-840
22. Hurvich C.M., and Chen W.W. An efficient taper for potentially overdifferenced long-memory time series. J. Time Ser. Anal. 21 2 (2000) 155-180
23. Hurvich C.M., Moulines E., and Soulier P. The FEXP estimator for potentially non-stationary linear time series. Stochastic Process. Appl. 97 2 (2002) 307-340
24. Hurvich C.M., Lang G., and Soulier P. Estimation of long memory in the presence of a smooth nonparametric trend. J. Amer. Statist. Assoc. 100 471 (2005) 853-871
25. Hurvich C.M., Moulines E., and Soulier P. Estimating long memory in volatility. Econometrica 73 4 (2005) 1283-1328
26. Hurvich C.M., and Ray B.K. Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. J. Time Ser. Anal. 16 1 (1995) 17-41
27. Johnson N.L., and Kotz S. Distributions in statistics. Continuous univariate distributions. 2 (1970), Houghton Mifflin Co., Boston, MA
28. Kaplan L.M., and Kuo C.-C.J. Fractal estimation from noisy data via discrete fractional Gaussian noise (DFGN) and the Haar basis. IEEE Trans. Signal Process. 41 12 (1993) 3554-3562
29. Kim, C.S., Phillips, P.C.B., 1999. Log periodogram regression: the nonstationary case. Tech. Rep. Cowles foundation discussion paper, Yale University. URL: http://cowles.econ.yale.edu
30. Künsch H. Statistical aspects of self-similar processes. Proceedings of the 1st World Congress of the Bernoulli Society, Vol. 1 (Tashkent, 1986) (1987), VNU Sci. Press, Utrecht 67-74
31. Lahiri S.N. A necessary and sufficient condition for asymptotic independence of discrete Fourier transforms under short- and long-range dependence. Ann. Statist. 31 2 (2003) 613-641
32. Mallat S. A Wavelet Tour of Signal Processing (1998), Academic Press Inc, San Diego, CA
33. McCoy E.J., and Walden A.T. Wavelet analysis and synthesis of stationary long-memory processes. J. Comput. Graph. Statist. 5 1 (1996) 26-56
34. Moulines E., Roueff F., and Taqqu M.S. Central Limit Theorem for the log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Fractals 15 4 (2007) 301-313
35. Moulines E., Roueff F., and Taqqu M.S. On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter. J. Time Ser. Anal. 28 2 (2007)
36. Moulines E., Roueff F., and Taqqu M. A wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series. Ann. Statist. 36 4 (2008) 1925-1956
37. Moulines E., and Soulier P. Semiparametric spectral estimation for fractional processes. Theory and Applications of Long-range Dependence (2003), Birkhäuser Boston, Boston, MA 251-301
38. Percival D.B., Sardy S., and Davison A.C. Wavestrapping time series: adaptive wavelet-based bootstrapping. Nonlinear and Nonstationary Signal Processing (Cambridge, 1998) (2000), Cambridge Univ. Press, Cambridge 442-471
39. Percival D.B., and Walden A.T. Wavelet methods for time series analysis. Cambridge Series in Statistical and Probabilistic Mathematics vol. 4 (2006), Cambridge University Press, Cambridge Reprint of the 2000 original [MR1770693]
40. Robinson P.M. Efficient tests of nonstationary hypotheses. J. Amer. Statist. Assoc. 89 428 (1994) 1420-1437
41. Robinson P.M. Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 (1995) 1630-1661
42. Robinson P.M. Log-periodogram regression of time series with long range dependence. Ann. Statist. 23 (1995) 1048-1072
43. Robinson P.M., and Henry M. Higher-order kernel semiparametric M-estimation of long memory. J. Econom. 114 1 (2003) 1-27
44. Roueff, F., Taqqu, M.S., 2008. Asymptotic normality of wavelet estimators of the memory parameter for linear processes. Tech. Rep. HAL/arXiv (submitted for publication). URL: http://fr.arxiv.org/abs/0805.0778
45. Samorodnitsky G., and Taqqu M.S. Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance (1994), Chapman and Hall
46. Serroukh A., Walden A.T., and Percival D.B. Statistical properties and uses of the wavelet variance estimator for the scale analysis of time series. J. Amer. Statist. Assoc. 95 449 (2000) 184-196
47. Shimotsu K., and Phillips P.C.B. Exact local Whittle estimation of fractional integration. Ann. Statist. 33 4 (2005) 1890-1933
48. Shimotsu K., and Phillips P.C.B. Local Whittle estimation of fractional integration and some of its variants. J. Econom. 130 2 (2006) 209-233
49. Stoev S., Taqqu M.S., Park C., Michailidis G., and Marron J.S. LASS: A tool for the local analysis of self-similarity. Comput. Statist. Data Anal. 50 9 (2006) 2447-2471
50. Tanaka K. The nonstationary fractional unit root. Econometric Theory 15 4 (1999) 549-582
51. Teyssière G., and Abry P. Wavelet analysis of nonlinear long-range dependent processes. Long Memory in Economics. Applications to Financial Time Series (2007), Springer, Berlin 173-238
52. Veitch D., and Abry P. A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Trans. Inform. Theory 45 3 (1999) 878-897
53. Veitch D., Abry P., and Taqqu M.S. On the automatic selection of the onset of scaling. Fractals 11 4 (2003) 377-390
54. Veitch D., Taqqu M.S., and Abry P. Meaningful MRA initialisation for discrete time series. Signal Processing 80 (2000) 1971-1983
55. Velasco C. Gaussian semiparametric estimation of non-stationary time series. J. Time Ser. Anal. 20 1 (1999) 87-127
56. Velasco C. Non-stationary log-periodogram regression. J. Econom. 91 2 (1999) 325-371
57. Velasco C. Non-Gaussian log-periodogram regression. Econom. Theory 16 1 (2000) 44-79
58. Velasco C., and Robinson P.M. Whittle pseudo-maximum likelihood estimation for nonstationary time series. J. Amer. Statist. Assoc. 95 452 (2000) 1229-1243
59. Wornell G.W., and Oppenheim A.V. Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process. 40 3 (1992) 611-623
60. Žurbenko I. On the efficiency of estimates of a spectral density. Scand. J. Statist. 6 2 (1979) 49-56