Hostname: page-component-89b8bd64d-9prln Total loading time: 0 Render date: 2026-05-12T09:26:24.735Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-memory continuous-time correlation models

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Chunsheng Ma
Chunsheng Ma*
Affiliation:
Wichita State University
*
∗ Postal address: Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA. Email address: cma@math.twsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper introduces a rather general class of stationary continuous-time processes with long memory by randomizing the time-scale of short-memory processes. In particular, by randomizing the time-scale of continuous-time autoregressive and moving-average processes, many power-law decay and slow decay correlation functions are obtained.

Keywords

Continuous-time autoregressive and moving-average processlong-range dependencepower-law decayshort-range dependenceslow decayOrnstein–Uhlenbeck process

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1133 - 1146
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Andersen, T., and Bollerslev, T. (1997). Heterogeneous information arrivals and return volatility dynamics: uncovering the long-run in high frequency returns. J. Finance 52, 975–1005.Google Scholar
Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. J. Econometrics 73, 5–59.CrossRefGoogle Scholar
Barndorff-Nielsen, O. E. (2000). Superposition of Ornstein—Uhlenbeck type processes. Theory Prob. Appl. 45, 175–194.CrossRefGoogle Scholar
Barndorff-Nielsen, O. E. and Shephard, N. (2001). Non-Gaussian Ornstein—Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Statist. Soc. B 63, 167–241.CrossRefGoogle Scholar
Bateman, H. (1954). Tables of Integral Transforms, Vol. 1. McGraw Hill, New York.Google Scholar
Brockwell, P. J. (2001). Continuous-time ARMA processes. In Handbook of Statistics, Vol. 19, Stochastic Processes: Theory and Methods, eds Shanbhag, D. N. and Rao, C. R., North-Holland, Amsterdam, pp. 249–276.Google Scholar
Comte, F., and Renault, E. (1996). Long memory continuous time models. J. Econometrics 73, 101–149.CrossRefGoogle Scholar
Comte, F., and Renault, E. (1998). Long memory in continuous-time stochastic volatility models. Math. Finance 8, 291–323.CrossRefGoogle Scholar
Cox, D. R. (1984). Long-range dependence: a review. In Statistics: an Appraisal, eds David, H. A. and David, H. T., Iowa State University Press, pp. 55–74.Google Scholar
Cox, D. R. (1991). Long-range dependence, non-linearity and time irreversibility. J. Time Series Analysis 12, 329–335.CrossRefGoogle Scholar
Ding, Z., Granger, C. W. J., and Engle, R. F. (1993). A long memory property of stock market returns and a new model. J. Empirical Finance 1, 83–106.CrossRefGoogle Scholar
Doukhan, P., Oppenheim, G., and Taqqu, M. S. (eds) (2003). Theory and Applications of Long-range Dependence. Birkhäuser, Boston, MA.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2. John Wiley, New York.Google Scholar
Granger, C. W. J. (2000). Current perspectives on long-memory processes. Academic Econom. Papers 28, 1–16.Google Scholar
Granger, C. W. J., and Joyeux, R. (1980). An introduction to long-memory time series. J. Time Series Analysis 1, 15–30.CrossRefGoogle Scholar
Hosking, J. M. R. (1981). Fractional differencing. Biometrika 68, 165–176.CrossRefGoogle Scholar
Hosking, J. M. R. (1984). Modeling persistence in hydrological time series using fractional differencing. Water Resources Res. 20, 1898–1908.CrossRefGoogle Scholar
Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civ. Eng. 116, 770–799.CrossRefGoogle Scholar
Lobato, L., and Savin, N. E. (1998). Real and spurious long-memory properties of stock-market data. J. Business Econom. Statist. 16, 261–268.Google Scholar
Lowen, S. B., and Teich, M. C. (1990). Power-law shot noise. IEEE Trans. Inf. Theory 36, 1302–1318.CrossRefGoogle Scholar
Ma, C. (2002). Correlation models with long-range dependence. J. Appl. Prob. 39, 370–382.CrossRefGoogle Scholar
Martin, R. J., and Walker, A. M. (1997). A power-law model and other models for long-range dependence. J. Appl. Prob. 34, 657–670.CrossRefGoogle Scholar
Priestley, M. B. (1981). Spectral Analysis and Time Series, Vol. 1. Academic Press, San Diego, CA.Google Scholar