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Inferring the conditional mean. (English) Zbl 1164.62382
Summary: Consider a stationary real-valued time series \(\{X_n\}^{\infty}_{n=0}\) with a priori unknown distribution. The goal is to estimate the conditional expectation \(E(X_{n+1}| X_0,\dots,X_n)\) based on observations \((X_0,\dots,X_n)\) in a pointwise consistent way. It is well known that this is not possible for all values of \(n\). We estimate it along stopping times.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
62L15 Optimal stopping in statistics
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