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For questions about when and why an r-squared-style calculation yields a value below zero.
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Out-of-sample R square is NEGATIVE [closed]
The "Out-of-sample $R^2$" is defined as:
$$
R^2_{OOS} = 1 - \frac{\sum_{t=\tau}^T\left(Y_t - \hat{Y}_{t\vert t-1}\right)^2}{\sum_{t=\tau}^T\left(Y_t - \hat{\mu}_{t\vert t-1}\right)^2}
$$
Where $\hat{Y …