Strongly consistent online forecasting of centered Gaussianprocesses |
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Authors: | Schafer D |
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Affiliation: | Math. Inst., Stuttgart Univ.; |
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Abstract: | An estimator E?(dn,n) of the conditional expectation EXn+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 |E?(dn,n)-EXn+1|Xn ,...,X(n-dn+1)]|→0 with probability 1. In addition, sufficient conditions for |EXn+1|Xn,X n-1,...]-EXn+1|Xn,...,X(n-dn +1)]| →0 to hold with probability 1 are given, that is, conditions under which E?(dn,n) can be used as a strongly consistent forecaster for |EXn+1|Xn,X n-1,...] |
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