I am capturing the daily percentage returns of a stock index with dummy variables. I do this both including and excluding the intercept. I get quite different results.
If I keep the intercept (image below), I will have less number of significant explanatory variables and my ARCH and GARCH terms sum to > 1.
On the other hand, if I drop the intercept, I get more significant variables and ARCH GARCH sum < 1.
Is it safe to assume that dropping the intercept gives us a better model? What does a sum of ARCH and GARCH > 1 imply and does this make the model inaccurate?
Best Answer
First of all, in both cases
arch L1.
+garch L1.
is actually below 1 (although very close to 1). Or am I reading the table incorrectly?Second, if
arch L1.
+garch L1.
were above one (hypothetically), that would mean the variance is increasing over time, and the increase is exponential (explosive). This is undesirable.Third, I would keep the constant in the model. The argumentation is analogous to keeping a constant in the conditional mean model: you care what moves the dependent variable away from its normal level (its mean) rather than from an arbitrary level of zero. It is similar with variance. You care about how the shocks move the conditional variance above the baseline, not above zero (zero variance is not a natural baseline, to put it loosely).Third, the intercept of a GARCH model should be kept in the model for the following reasons.
Fourth, significance of variables is not a very strong statistical argument for choosing one model over the other. Although your boss might be more impressed if you show her a model with significant regressors, that does not mean the model would reflect the reality better. If models were chosen by significance of variables, spurious results would be widespread. (Oh, but this is actually what is happening in reality!). Instead of looking at significance of variables,
look at model residuals. Check whether they match the model assumptions and are well behaved.use information criteria or cross validation for model selection. (E.g. if your goal is forecasting, pick a model with the lowest AIC or the lowest test error in leave-one-out cross validation; but note that in time series, cross validation is more complicated than in the cross sectional setting, and information criteria are the considerably easier option to use.)