I would like to check my understanding of the Chow Forecast test.The test is used to perform a test on the following models: $y_1=\beta X+\epsilon_1$ and $y_2=\beta X+ \nu + \epsilon_2$, with $H_0:\nu=0$ and $H_1: \nu\neq 0$.

Now I wonder whether that means that the following holds true: \begin{align*} F&=\frac{(e_R'e_R-e_1'e_1)/g}{e_1'e_1/(n-k)}\\ &=\frac{\left(\sum\limits_{i=1}^{n+g} (y_i-x_i'\beta)^2-\sum\limits_{i=1}^n (y_i-x_i'\beta)^2 \right)/g}{\sum\limits_{i=1}^n (y_i-x_i'\beta)/(n-k)}\\ &=\frac{\sum\limits_{i=n}^{n+g} (y_i-x_i'\beta)^2/g}{\sum\limits_{i=1}^n (y_i-x_i'\beta)/(n-k)} \end{align*}

Are these true, and if not, why not?

  • $\begingroup$ Never mind. Question can be deleted. $\endgroup$ – abc Feb 2 '14 at 14:29
  • $\begingroup$ If you know the answer, please post it here; you can help other people that may stumble upon a similar problem. And earn some reputation. $\endgroup$ – user88 Feb 2 '14 at 15:26

If the $\beta$ in both regressions is the same then the numerator should say $\frac{\displaystyle\sum_{i=n+1}^{n+g}(y_i-x_i\beta)^2}{g}$ but I don't think they are. So they don't cancel out when you subtract one from the other.

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