Estimation of autocorrelation in a binary time series
type: Item
instance of: scholarly article
title: Estimation of autocorrelation in a binary time series
zbMATH Open document ID: 0663.62102
DOI: 10.1007/BF01544195
author: E. Damsleth
author: A. H. El-Shaarawi
published in: Stochastic Hydrology and Hydraulics
publication date: 1988-01-01T00:00:00Z
review text: Let \(Y_ t\) be a stationary Gaussian time series with zero mean. Define \(X_ t=1\) for \(Y_ t>0\) and \(X_ t=0\) for \(Y_ t<0\). The lag k transition probability \(\lambda_ k=P(X_ t=1| X_{t-k}=1)\) can be estimated by \[ {\hat \lambda}_ k=1-(n-k)^{- 1}\sum^{n}_{t=k+1}(X_ t+X_{t-k}-2X_ tX_{t-k}). \] The estimator \({\hat \lambda}{}_ k\) is unbiased. The authors derive a formula for var \({\hat \lambda}{}_ 1\), suggest three approximations to var \({\hat \lambda}{}_ 1\) in the AR(1) case and give an explicit formula for var \({\hat \lambda}{}_ 1\) in the MA(1) and MA(2) cases. In an appendix the authors investigate the probability that four dependent normal variables have the same sign. They reduce the general formula to a two-dimensional integral. If the series is an AR(1) process, then a good approximation to the probability is found.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 4084804
zbMATH Keywords: binary time series
zbMATH Keywords: variance
zbMATH Keywords: hard clipping
zbMATH Keywords: censored observations
zbMATH Keywords: autocorrelation
zbMATH Keywords: acid rain
zbMATH Keywords: stationary Gaussian time series
zbMATH Keywords: lag k transition probability
zbMATH Keywords: approximations
zbMATH Keywords: dependent normal variables
zbMATH Keywords: same sign
reviewed by: Jiří Anděl
MaRDI profile type: Publication
cites work: Q5598050
cites work: A note on the evaluation of the multivariate normal integral
cites work: Estimation of the Parameters in Stationary Autoregressive Processes after Hard Limiting
cites work: Q3859149
cites work: Q3227937
cites work: Rank correlation and product-moment correlation
cites work: A table of normal integrals
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description: scientific article; zbMATH DE number 4084804