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Q173Section III (Statistics)173 of 190

The one-step-ahead AR(1) forecast-error ratio is always strictly positive

Let {Xt}\{X_t\} be a stationary AR(1) time series given by the recursive equation Xt=ϕXt−1+ZtX_t=\phi X_{t-1}+Z_t, where Zt∼WN(0,σ2)Z_t\sim WN(0,\sigma^2). Let P3X4P_3X_4 represent the forecast of X4X_4 given the observations (X1,X2,X3)(X_1,X_2,X_3). If C(ϕ)C(\phi) is defined as C(ϕ)=E(X4−P3X4)2E(X4−E(X4))2C(\phi)=\dfrac{E(X_4-P_3X_4)^2}{E(X_4-E(X_4))^2}, then which of the following is not true?

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