Long range dependence, unbalanced Haar wavelet transformation and changes in local mean level

International Journal of Wavelets, Multiresolution and Information Processing

Volumn 7, Issue 1, 2009, Pages 23-58

  Baek, Changryong ^a   Pipiras, Vladas ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Changes in local mean level; Long range dependence; Unbalanced Haar wavelet transformation

Indexed keywords

CHANGES IN LOCAL MEAN LEVEL; DATA TRAFFICS; KERNEL SMOOTHING; LONG RANGE DEPENDENCE; LONG TIME SERIES; LONG-RANGE DEPENDENTS; LRD PROPERTIES; NATURAL TOOLS; POISSON ARRIVAL PROCESS; REAL TIME SERIES; STATIONARY TIME SERIES; UNBALANCED HAAR WAVELET TRANSFORMATION;

TELECOMMUNICATION TRAFFIC;

TIME SERIES;

EID: 65449173521     PISSN: 02196913     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219691309002763     Document Type: Article

References (34)

1. P. Abry, P. Flandrin, M. S. Taqqu and D. Veitch, Self-similarity and long-range dependence through the wavelet lens, in Theory and Applications of Long-Range Dependence, eds. P. Doukhan, G. Oppenheim and M. S. Taqqu (Birkhäuser, 2003), pp. 527-556.
2. E. G. Altmann and H. Kantz, Recurrence time analysis, long-term correlations, and extreme events, Phys. Rev. E. 71(5) (2005) 056106, 9 pp.
3. J. Beran, Statistics for Long-Memory Processes, Monographs on Statistics and Applied Probability, Vol. 6 (Chapman and Hall, New York, 1994).
4. I. Berkes, L. Horváth, P. Kokoszka and Q.-M. Shao, On discriminating between long-range dependence and changes in mean, Ann. Statist. 34(3) (2006) 1140-1165.
5. N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, Vol. 27 (Cambridge University Press, Cambridge, 1989).
6. C. Bos, P. Franses and M. Ooms, Long memory and level shifts: Re-analyzing inflation rates, Empirical Econometrics 24(3) (1999) 427-449.
7. A. Ciancio, Analysis of time series with wavelets, Int. J. Wavelets Multiresolut. Inf. Process. 5(2) (2007) 241-256.
8. F. X. Diebold and A. Inoue, Long memory and regime switching, J. Econometrics 105(1) (2001) 131-159.
9. P. Doukhan, G. Oppenheim and M. S. Taqqu (eds.), Theory and Applications of Long-Range Dependence (Birkhäuser, 2003).
10. P. Flandrin, Wavelet analysis and synthesis of fractional Brownian motion, IEEE Trans. Inform. Theory 38(2, part 2) (1992) 910-917.
11. G. B. Folland, Real Analysis, 2nd edn. (John Wiley & Sons Inc., New York, 1999).
12. P. Fryzlewicz, Unbalanced Haar technique for nonparametric function estimation, J. Amer. Statist. Assoc. 102(480) (2007) 1310-1327.
13. L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière, Rescaled variance and related tests for long memory in volatility and levels, J. Econometrics 112(2) (2003) 265-294.
14. P. W. Glynn and W. Whitt, Large deviations behavior of counting processes and their inverses, Queueing Syst. 17(1-2) (1974) 107-128.
15. C. W. J. Granger and N. Hyung, Occasional structural breaks and long memory, Economics Working Paper Series 99-14, Department of Economics, University of California at San Diego (1999).
16. C. W. J. Granger and R. Joyeux, An introduction to long-memory time series models and fractional differencing, J. Time Ser. Anal. 1 1) (1980) 15-29.
17. S. Hariz, J. Wylie and L. Zhang, Optimal rate of convergence for nonparametric change-point estimators for non-stationary sequences, Ann. Statist. 35(4) (2007) 1802-1826.
18. T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics (Springer-Verlag, 2001).
19. J. R. M. Hosking, Fractional differencing, Biometrika 68(1) (1981) 165-176.
20. P. Hurst, Long term storage capacity of reservoirs, Trans. Amer. Soc. Civil Engineers 116 (1951) 770-808.
21. A. Jach and P. Kokoszka, Wavelet domain test for long-range dependence in the presence of a trend, Statistics 42(2) (2008) 101-113.
22. V. Klemeš, The Hurst pheomenon: A puzzle?, Water Resour. Res. 10(4) (1974) 675-688.
23. C.-M. Kuan and C.-C. Hsu, Change-point estimation of fractionally integrated processes, J. Time Ser. Anal. 19(6) (1998) 693-708.
24. E. A. Maharaj, Using wavelets to compare time series patterns, Int. J. Wavelets Multiresolut. Inf. Process. 3(4) (2005) 511-521.
25. B. B. Mandelbrot, Limit theorems on the self-normalized range for weakly and strongly dependent processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 31 (1975) 271-285.
26. B. B. Mandelbrot and J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422-437.
27. B. B. Mandelbrot and J. R. Wallis, Computer experiments with fractional Gaussian noises. Part 1: Sample graphs, averages and variances, Water Resour. Res. 5 (1969) 228-241.
28. T. Mikosch and C. Stǎricǎ, Changes of structure in financial time series and the Garch model, REVSTAT 2(1) (2004) 41-73.
29. K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (John Wiley & Sons, Inc., New York, 2000).
30. A. A. Puhalskii and W. Whitt, Functional large deviation principles for first-passage-time processes, Ann. Appl. Probab. 7(2) (1997) 362-381.
31. S. Resnick, Adventures in Stochastic Processes (Birkhäuser Boston Inc., Boston, MA, 1992).
32. D. Veitch and P. Abry, A wavelet-based joint estimator of the parameters of long-range dependence, IEEE Trans. Inform. Theory 45(3) (1999) 878-897.
33. S. Veres and M. Boda, The chaotic nature of TCP congestion control, Proc. IEEE INFOCOM, Vol. 3, Tel Aviv, Israel (2000), pp. 1715-1723.
34. H. Wright, Testing for a structural break at unknown date with long-memory disturbances, J. Time Ser. Anal. 19(3) (1998) 369-376.