Abstract
The properties of the well known estimator of the transition probabilities in a binary time series are investigated. A formula for the variance is obtained, which generally involves a double integral. However, in the case when the binary series is obtained by hard clipping of an AR(1) process, a good and fairly simple approximation is derived. In the MA(1) or MA(2) case exact formulae for the variance is given. In the appendix an excellent approximation to the fourth order cumulant of a clipped AR(1) process is derived, which may be of interest in other applications as well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cox, D.R. 1970: The analysis of binary data. Methuen & Co., Ltd., London
David, F.N. 1953: A note on the evaluation of the multivariate normal integral. Biometrika 40, 458–459
El-Shaarawi, A.H.; Damsleth, E. 1987: Parametric and nonparametric tests for dependent data. Submitted to the Water Resour. Bulletin
Kedem, B. 1980: Estimation of the parameters in stationary AR processes after hard limiting. JASA 75, 146–153
Kedem, B. 1980: Binary time series. M. Dekker, New York
Lommicki, Z.A.; Zaremba, S.K. 1955: Some applications of zero-one processes. JRSS B 17, 243–255
Moran, P.A.P. 1948: Rank correlation and product moment correlation. Biometrika 35, 203–206
Owen, D.B. 1980: A table of normal integrals. Communications in Statistics, B9, 389–419
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Damsleth, E., El-Shaarawi, A.H. Estimation of autocorrelation in a binary time series. Stochastic Hydrol Hydraul 2, 61–72 (1988). https://doi.org/10.1007/BF01544195
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01544195