Contents
What are the assumptions of ARCH and GARCH?
The basic version of the least squares model assumes that, the expected value of all error terms when squared, is the same at any given point. This assumption is called homoskedasticity and it is this assumption that is the focus of ARCH/GARCH models.
What is the difference between ARIMA and ARCH?
An ARCH model is very similar to ARIMA, but its CH component models the previous squared resisduals at each previous point in time. We are using the term “volatility” here as a proxy for variance or squared residuals. The CH model is predicting a future squared residual as part of the wider ARCH model.
What are the steps required to estimate an ARCH Garch model?
The general process for a GARCH model involves three steps. The first is to estimate a best-fitting autoregressive model. The second is to compute autocorrelations of the error term. The third step is to test for significance.
What’s the difference between the arch and ARIMA models?
An ARCH model is very similar to ARIMA, but its CH component models the previous squared resisduals at each previous point in time. We are using the term “volatility” here as a proxy for variance or squared residuals. The CH model is predicting a future squared residual as part of the wider ARCH model.
Which is the natural way to use arch / GARCH?
Therefore, in my opinion, the natural way to employ ARCH/GARCH is that after building an ARIMA model, if we found residuals with inconstant variance, we fit an ARCH/GARCH process to the variance of residuals (However, like I asked above, inconstant variance is barely, if not never, checked as an assumption). Somehow follow-up question of 2.
How to fit a GARCH model to an arch model?
Let’s use the fGarch package to fit a GARCH (1,1) model to x where we center the series to work with a mean of 0 as discussed above. The fGarch summary provides the Jarque Bera Test for the null hypothesis that the residuals are normally distributed and the familiar Ljung-Box Tests. Ideally all p-values are above 0.05. Diagnostics all look okay.
How can I re-fit my Arima + GARCH model?
In practice, if you discover that the residuals have a GARCH structure, what you do is you first identify the order of the GARCH structure and then re-fit your ARIMA+GARCH model simultaneously (in one shot). You can do this using the rugarch library in R, for example.