It is said that in order to combine garch models with arima models, their results are added together, while garch results are positive in every step. Is there anything wrong with this combination? We have positive and negative numbers in terms of errors, so what will happen to negative errors in the combination of these models?
I don't see your problem. In standard ARIMA models, the errors are independent (or simply uncorrelated) random variables with a zero mean and a constant variance, say sigma^2. In an ARIMA-GARCH model, the variance is no longer constant but is driven by a GARCH model. That means that the variance at time t, sigma_t^2 say, is a linear combination of past variances and of past squared errors. So we have a conditionally heteroscedastic model. You can see examples of ARMA-ARCH models in Weiss (1986) paper in the Journal of Time Series Analysis 5, 129-143.
- Badges
- Science topic
- Similar topics
- Correction