I have created a VAR model in R (using the command VAR) and my model reports an R-squared of about 0.8 for the variable I'm most interested in. I'm trying to replicate that result by calculating the R-squared by hand. I have extracted the fitted values (using the command fitted(model_name)) and then I have used the following equation:
$$R^2 = 1- { \sum_{} (y-\hat y)^2 \over \sum_{}(y - \overline y)^2}.$$$$R^2 = 1- { \sum_{t} (y_t-\hat y_t)^2 \over \sum_{t}(y_t - \overline y)^2},$$
Withwith $y$$y_t$ = actual value, $ \hat y$$ \hat y_t$ = predicted (fitted) value and $ \overline y$ = the average of the actual value.
I am taking into account the fact that my model uses two lags, so I have two fitted values less than the total amount of points used to train. I'm making sure to pair the actual and predicted values correctly.
I have tried using this equation before in regular linear regression and I am able to replicate the value I get from R, however I cannot do it with this VAR model. Is it because when the R-squared is calculated for time series, something different is done? I have tried googling this and cannot find any reference to a different equation for the case of time series.
Any comments or suggestions as to what could be wrong will be greatly appreciated.
