# zbMATH — the first resource for mathematics

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
##### Keywords:
stationary processes