Abstract
The sample autocorrelation function (acf) is an important statistic in time series analysis. It is frequently relied upon for assessing the dependence structure of a time series and may also be used for model identification and parameter estimation in the class of ARMA models. In this paper, we review some of the main asymptotic results for sample acfs of infinite order moving averages. While the classical theory concerning sample acfs requires the process to have at least finite second moments, our main interest in this paper will be the case when the process has an infinite variance. It turns out that in the infinite variance case, the sample acf can have desirable large sample properties and these can be helpful in estimating various parameters associated with the model.
This research was partially supported by NSF grant MCS 8501763.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, T.W. (1971). Statistical Analysis of Time Series. Wiley, New York.
Choyer, J., Ney, P. and Wainger, S. (1973). Functions of probability measures. J. Analyse Math. 26, 255–302.
Cline, D. (1983). Estimation and linear prediction for regression, autoregression and ARMA with infinite variance data. Ph.D. Thesis, Department of Statistics, Colorado State University, Fort Collins, CO 80523.
Davis, R.A. and Resnick, S. (1984). Limit theory for the sample covariance and correlation functions of moving averages. (To appear in Annals of Statistics)
Davis, R.A. and Resnick, S. (1985). More limit theory for the sample correlation function of moving averages. (To appear in Stochastic Processes and Their Applications.)
Embrechts, P. and Goldie, C. (1980). On closure and factorization properties of subexponential and related distributions. J. Austral. Math. Soc. ( Series A ), 29, 243–256.
Feller, W. (1971). An Introduction to Probability Theory and its Applications. Vol. II, 2nd edition, Wiley, New York.
Fuller, W. (1976). Introduction to Statistical Time Series. Wiley, New York.
Haan, L. de, Omey, E. and Resnick, S. (1984). Domains of attraction and regular variation inlrd. J. Mult. Analysis, 14, 17–33.
Hannan, E.J. and Kanter, M. (1977). Autoregressive processes with infinite variance. J. Appl. Probability, 14, 411–415.
Kanter, M. and Steiger, W.L. (1974). Regression and autoregression with infinite variance. Advances in Appl. Probability, 6, 768–783.
Mailer, R. (1981). A theorem on products of random variables with applications to regression. Austral. J. Statist., 23, 177–185.
Yohai, V. and Maronna, R. (1977). Asymptotic behavior of least-squares estimates for autoregressive processes with infinite variances. Ann. Statistics, 5, 554–560.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media New York
About this chapter
Cite this chapter
Davis, R., Resnick, S. (1986). Limit Theory for the Sample Correlation Function of Moving Averages. In: Eberlein, E., Taqqu, M.S. (eds) Dependence in Probability and Statistics. Progress in Probability and Statistics, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8162-8_19
Download citation
DOI: https://doi.org/10.1007/978-1-4615-8162-8_19
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4615-8163-5
Online ISBN: 978-1-4615-8162-8
eBook Packages: Springer Book Archive