Intermittent estimation for Gaussian processes
IEEE Transactions on Information Theory
Long-term prediction intervals of time series
IEEE Transactions on Information Theory
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An estimator Eˆ(dn,n) of the conditional expectation E[Xn+1|Xn,...,X(n-dn+1)] in a centered, stationary, and ergodic Gaussian process {Xi}i with absolutely summable Wold coefficients is constructed on the basis of having observed X1,...,Xn . For a suitable choice of the length dn→∞ (n→∞) of the past covered by the conditional expectation, it is established that |Eˆ(dn,n)-E[Xn+1|Xn ,...,X(n-dn+1)]|→0 with probability 1. In addition, sufficient conditions for |E[Xn+1|Xn,X n-1,...]-E[Xn+1|Xn,...,X(n-dn +1)]| →0 to hold with probability 1 are given, that is, conditions under which Eˆ(dn,n) can be used as a strongly consistent forecaster for |E[Xn+1|Xn,X n-1,...]