The integrated periodogram for long-memory processes with finite or infinite variance

Stochastic Processes and their Applications

Volumn 66, Issue 1, 1997, Pages 55-78

  Kokoszka, P ^a   Mikosch, T ^b  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Fractional ARIMA; Functional limit theorems; Goodness of fit tests; Heavy tails; Integrated periodogram; Long memory

Indexed keywords

EID: 0031065859     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00124-X     Document Type: Article

References (35)

1. T.W. Anderson, Goodness of fit tests for spectral distributions, Ann. Statist 21 (1993) 830-847.
2. M.S. Bartlett, Problemes de l'analyse spectrale des séries temporelles stationnaires, Publ. Inst. Statist. Univ. Paris III-3 (1954) 119-134.
3. M.S. Bartlett, An Introduction to Stochastic Processes with Special Reference to Methods and Applications (Cambridge University Press, Cambridge, 1955).
4. J. Beran, Statistics for Long-Memory Processes (Chapman & Hall, New York, 1994).
5. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
6. N.H, Bingham, C.M. Goldie and J.L. Teugels, Regular Variation (Cambridge University Press, Cambridge, 1987).
7. P.J. Brockwell and R.A. Davis, Time Series: Theory and Methods (Springer, New York, 2nd ed., 1991).
8. R. Dahlhaus, Asymptotic normality of spectral estimates, J. Multivariate Anal. (1985) 16, 412-431.
9. R. Dahlhaus, Empirical spectral processes and their applications to time series analysis, Stochastic Process Appl. 30 (1988) 69-83.
10. R.A. Davis and S.I. Resnick, Limit theory for moving averages of random variables with regularly varying tail probabilities, Ann. Probab. 13 (1985) 179-195.
11. R.A. Davis and S.I. Resnick, Limit theory for the sample covariance and correlation functions of moving averages, Ann. Statist. 14 (1986) 533-558.
12. W. Feller, An Introduction to Probability Theory and its Applications II (Wiley, New York, 1971).
13. L. Giraitis and R. Leipus, A functional central limit theorem for non-parametric estimates of spectra and the change-point problem for spectral functions, Lith. Math. Trans. (Lit. Mat. Sb.) 30 (1990) 674-697.
14. L. Giraitis and R. Leipus, Testing and estimating in the change-point problem of the spectral function, Lith. Math. Trans. (Lit. Mat. Sb.) 32 (1992) 20-38.
15. L. Giraitis, R. Leipus and D. Surgailis, The change-point problem for dependent observations, J. Statist. Plann. Inference [To appear].
16. L. Giraitis and D. Surgailis (1994) A central limit theorem for the empirical process of a long memory linear sequence, Probab. Theory Related Fields [To appear].
17. U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series (Chelsea Publishing Co., New York, 2nd ed., 1984).
18. T. Hida, Brownian Motion (Springer, New York, 1980).
19. L. Horváth and P. Kokoszka, The effect of long-range dependence on change-point estimators, J. Statist. Plann. Inference [To appear].
20. C. Klüppelberg and T. Mikosch, The integrated periodogram for stable processes, Ann. Statist. [To appear].
21. C. Klüppelberg and T. Mikosch, Gaussian limit fields for the integrated periodogram, Ann. Appl. Probab. [To appear].
22. P.S. Kokoszka, Prediction of infinite variance fractional ARIMA, Probab. Math. Statist. 16 (1996) 65-83.
23. P.S. Kokoszka and M.S. Taqqu, Fractional ARIMA with stable innovations, Stochastic Process Appl. 60 (1995) 19-47.
24. P.S. Kokoszka and M.S. Taqqu, Parameter estimation for infinite variance fractional ARIMA, Ann. Statist. [To appear].
25. P.S. Kokoszka and M.S. Taqqu, Discrete time parametric models with long memory and infinite variance, Preprint (1996).
26. T.R. McConnell and M.S. Taqqu, Decoupling inequalities for multilinear forms in independent symmetric random variables, Ann. Probab. 14 (1986) 943-954.
27. T. Mikosch, Functional limit theorems for random quadratic forms, Stochastic Process Appl. 37 (1991) 81-98.
28. T. Mikosch, T. Gadrich, C. Klüppelberg and R.J. Adler, Parameter estimation for ARMA models with infinite variance innovations, Ann. Statist. 23 (1995) 305-326.
29. T. Mikosch and R. Norvaiša, Uniform convergence of the empirical spectral distribution function, Preprint (1995).
30. M.B. Priestley, Spectral Analysis and Time Series I (Academic Press, New York, 1981).
31. J. Rosinski, Remarks on Banach spaces of stable type, Probab. Math. Statist. 1 (1980) 67-71.
32. J. Rosinski and W.A. Woyczyński, Multilinear forms in Pareto-like random variables and product random measures, Coll. Math. 51 (1987) 303-313.
33. G. Samorodnitsky and M.S. Taqqu, Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance (Chapman and Hall, London, 1994).
34. G.R. Shorack and J.A. Wellner, Empirical Processes with Applications to Statistics (Wiley, New York, 1986).
35. A. Zygmund, Trigonometric Series (Cambridge University Press, Cambridge, 1st paperback ed., 1988).