Maximum likelihood estimation of linear continuous time long memory processes with discrete time data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 67, Issue 5, 2005, Pages 703-716

  Tsai, Henghsiu ^a,c   Chan, K S ^b  

^a ACADEMIA SINICA   (Taiwan)

^b UNIVERSITY OF IOWA   (United States)

^c INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Continuous time autoregressive fractionally integrated moving average models; Fractional Brownian motion; Innovations algorithm; Irregularly spaced data; Polynomial trend

Indexed keywords

EID: 28044436709     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00522.x     Document Type: Article

References (37)

1. Baillie, R. (1996) Long memory processes and fractional integration in econometrics. J. Econometr., 73, 5-59.
2. Beran, J. (1994) Statistics for Long-memory Processes. New York: Chapman and Hall.
3. Beran, J. (1995) Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models. J. R Statist. Soc. B, 57, 659-672.
4. Bloomfield, P. (1992) Trends in global temperature. Clim. Change, 21, 1-16.
5. Brockwell, P. J. (1993) Threshold ARMA processes in continuous time. In Dimension Estimation and Models (ed. H. Tong), pp. 170-190. River Edge: World Scientific.
6. Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. New York: Springer.
7. Brockwell, P. J. and Marquardt, T. (2005) Lévy-driven and fractionally integrated ARMA processes with continuous time parameter. Statist. Sin., 15, 477-494.
8. Chambers, M. J. (1996) The estimation of continuous parameter long-memory time series models. Econometr. Theory, 12, 374-390.
9. Comte, F. (1996) Simulation and estimation of long memory continuous time models. J. Time Ser. Anal., 17, 19-36.
10. Comte, F. and Renault, E. (1996) Long memory continuous time models. J. Econometr., 73, 101-149.
11. Dahlhaus, R. (1989) Efficient parameter estimation for self-similar processes. Ann. Statist., 17, 1749-1766.
12. Dahlhaus, R. (1995) Efficient location and regression estimation for long range dependent regression models. Ann. Statist., 23, 1029-1047.
13. Dahlhaus, R. (2004) Correction note for efficient parameter estimation for self-similar processes. Working Paper. Universität Heidelberg, Heidelberg.
14. Davies, R. B. and Harte, D. S. (1987) Tests for Hurst effect. Biometrika, 74, 95-101.
15. Duncan, T. E., Hu, Y. and Pasik-Duncan, B. (2000) Stochastic calculus for fractional Brownian motion: I, theory. SIAM J. Control Optimzn, 38, 582-612.
16. Efron, B. and Tibshirani R. J. (1993) An Introduction to the Bootstrap. New York: Chapman and Hall.
17. Elliott, R. and van der Hoek, J. (2003) A general fractional white noise theory and applications to finance. Math. Finan., 13, 301-330.
18. Granger, C. W. J. and Joyeux, R. (1980) An introduction to long memory time series models and fractional differencing. J. Time Ser. Anal., 1, 15-29.
19. Hosking, J. R. M. (1981) Fractional differencing. Biometrika, 68, 165-176.
20. Hu, Y. and Øksendal, B. (2003) Fractional white noise calculus and application to finance. Inf. Dimen. Anal. Quant. Probab. Reltd Top., 6, 1-32.
21. Ling, S. and Li, W. K. (1997) On fractionally integrated autoregressive moving-average time series models with conditional heteroscedascity. J. Am. Statist. Ass., 92, 1184-1194.
22. Mandelbrot, B. B. and Van Ness, J. W. (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev., 10, 422-437.
23. Øksendal, B. (2003) Fractional Brownian motion in finance. Pure Mathematics Preprint Ser. 2003, no. 28. University of Oslo, Oslo. (Available from http://www.math.uio.no/eprint/pure_math/2003/28-03.pdf.)
24. Palma, W. and Chan, N. H. (1997) Estimation and forecasting of long-memory processes. J. Forecast., 16, 395-410.
25. Palma, W. and Del Pino, G. (1999) Statistical analysis of incomplete long-range dependent data. Biometrika, 86, 965-972.
26. Priestley, M. B. (1981) Spectral Analysis and Time Series. London: Academic Press.
27. Ray, B. K. and Tsay, R. S. (1997) Bandwidth selection for kernel regression with long-range dependent errors. Biometrika, 84, 791-802.
28. Robinson, P. M. (1993) Time series with strong dependency. In Advances in Econometrics: Proc. 6th Wrld Congr. (ed. C. A. Sims), pp. 47-95. Cambridge: Cambridge University Press.
29. Rudin, W. (1976) Principles of Mathematical Analysis. New York: McGraw-Hill.
30. Shapiro, H. S. and Silverman, R. A. (1960) Alias-free sampling of random noise. J. Soc. Industrl Appl. Math., 8, 225-248.
31. So, M. K. P. (1999) Time series with additive noise. Biometrika, 86, 474-482.
32. Sowell, F. (1992) Modeling long-run behaviour with the fractional ARMA model. J. Monet. Econ., 29, 277-302.
33. Stramer, O., Tweedie, R. L. and Brockwell, P. J. (1996) Existence and stability of continuous time threshold ARMA processes. Statist. Sin., 6, 715-732.
34. Tsai, H. and Chan, K. S. (2005a) Maximum likelihood estimation of a class of continuous-time long-memory processes. Technical Report 324. Department of Statistics and Actuarial Science, University of Iowa, Iowa City. (Available from http://www.stat.uiowa.edu/techrep/.)
35. Tsai, H. and Chan, K. S. (2005b) Quasi-maximum likelihood estimation for a class of continuous time long-memory processes. J. Time Ser. Anal., to be published.
36. Valkeila, E. (1999) On some properties of geometric fractional Brownian motion. Preprint. University of Helsinki, Helsinki.
37. Viano, M. C., Deniau, C. and Oppenheim, G. (1994) Continuous-time fractional ARMA processes. Statist. Probab. Lett., 21, 323-336.