Inferring the conditional mean

Details Inferring the conditional mean Inferring the conditional mean

2007-10-19

arxiv.org/abs/0710.3757v1

Theory Stoch. Process. 11 (2005), no. 1-2, pp. 112--120

Mathematics

Probability

Scientific paper

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

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