Inferring the conditional mean

Abstract

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.

Cited by in corpus (1)

• On Sequential Estimation and Prediction for Discrete Time Series