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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
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