Geodesic
Inferring the residual waiting time for binary stationary time series
Kybernetika, Tome 50 (2014) no. 6, pp. 869-882
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For a binary stationary time series define $\sigma_n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of $\sigma_n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.
For a binary stationary time series define $\sigma_n$ to be the number of consecutive ones up to the first zero encountered after time $n$, and consider the problem of estimating the conditional distribution and conditional expectation of $\sigma_n$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state the stopping times along which we estimate have density one.
DOI : 10.14736/kyb-2014-6-0869
Classification : 60G10, 60G25, 60G40, 60K05, 62G05, 62M10
Keywords: nonparametric estimation; stationary processes 
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Morvai, Gusztáv; Weiss, Benjamin. Inferring the residual waiting time for binary stationary time series. Kybernetika, Tome 50 (2014) no. 6, pp. 869-882. doi: 10.14736/kyb-2014-6-0869

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