General Variance Decomposition Applicable To Dynamic Systems
The following formula shows how to apply the general, measure theoretic variance decomposition formula to stochastic dynamic systems. Let Y(t) be the value of a system variable at time t. Suppose we have the internal histories (natural filtrations), each one corresponding to the history (trajectory) of a different collection of system variables. The collections need not be disjoint. The variance of Y(t) can be decomposed, for all times t, into c ≥ 2 components as follows:
The decomposition is not unique. It depends on the order of the conditioning in the sequential decomposition.
Read more about this topic: Law Of Total Variance
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