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Inferring the residual waiting time for binary stationary time series. (English) Zbl 1308.62067
Summary: 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.

##### MSC:
 62G05 Nonparametric estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G40 Stopping times; optimal stopping problems; gambling theory 60G25 Prediction theory (aspects of stochastic processes) 60G10 Stationary stochastic processes 60K05 Renewal theory
##### Keywords:
nonparametric estimation; stationary processes
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##### References:
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