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6033统计中等derivationmedium

Innovation Variance and a Standardized Surprise

题目

In the model yt=xt+vty_t=x_t+v_t with vtN(0,3)v_t\sim N(0,3), the predicted state at time tt is N(5,7)N(5,7). You then observe yt=11y_t=11. Compute the innovation (one-step forecast error) variance SS, and the standardized innovation (ytm)/S(y_t-m^-)/\sqrt{S}.

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Innovation Variance S

Standardized Innovation