On page 306, Tambakis and van Royen report an adjusted r2 for a GARCH(1,1) model. How is this possible? What are they reporting?
You can find the paper here
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Even if I don’t know exactly what the authors of the paper have done, sometimes I have seen something similar in my past by other authors and want to share with you a sense of what I remember. If you interpret the Garch estimated variance as a prediction for the squared difference between the series and its conditional mean, then you can compute the sum of such squares and interpret it as the sum of squared forecasting error of the Garch.. then you have the SSE that is used in the numerator of a an R2-like measure (1-SSE)/(TSS) and apply a penalization for the number of parameters. – Fr1 Aug 03 '19 at 11:47
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This is particularly intuitive when you have a non-significant conditional mean. in that case you can interpret the Garch forecasted variance as the prediction for the squared values of the process to be forecasted.. and then you can take the forecasting error and MSE of SSE and evaluate the goodness of fit.. please notice that it has been a while since I last dealt with Garch goodness of fit, so take it into account when you read my comment, but I hope this will give a sense.. they could have used a AIC/BIC, maybe it would have been more in line with the reminder of literature on Garch spec. – Fr1 Aug 03 '19 at 11:51