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Suppose I am also implementing an ARMA-GARCH process sequentially, so I am using the residuals from ARMA to optimize GARCH. … (I believe) Then it is assumed that the $\epsilon_i$ in both ARMA and GARCH follow the same distribution. …

However, my constant term in GARCH, $\omega$, seems to grow without bound as the optimization proceeds. … Is there any sort of constraint on the GARCH parameters other than they must all be non-negative and that $\alpha + \beta < 1$? …

Suppose we have a time series $\{y_t\}$ which we would like to model using an ARCH or GARCH model. … The point of both the ARCH and GARCH models is to model the conditional variance $\sigma_t^2$. If we use an ARCH model then the idea is to model $\sigma_t^2$ by using an AR model. …

From what I understand one begins with MA, then AR, then GARCH. … Once we have applied ARMA, are the innovations then fed into GARCH? My current understanding is the innovations from ARMA, $\epsilon_t$, are used in least squares to find the GARCH parameters. …

I am interested in fitting an ARMA-GARCH model to my data. After reading a few pages online I did so sequentially by first applying ARMA and then feeding the residuals into GARCH. … I then took the estimated mean from ARMA and variance from GARCH to construct a forecast. …

I wish to fit the innovations resulting from a GARCH (1,1) process to either a student-t or an NIG distribution. For stability, I had to scale my data before applying GARCH. … I have taken a look at another post addressing a similar question (Does $\delta$ parameter in GARCH-M stay unchanged when the process is scaled?) but they assume a normal distribution. …

I've made a few posts regarding a manual ARMA GARCH implementation and I have made some great progress. However, I am still shy of a working program as I am obtaining some rather large forecasts. … Instead of using OLS for the ARMA, I am instead constructing ARMA GARCH simultaneously. …

For numerical stability, I thought it might be a good idea to scale my data before feeding them into an ARMA GARCH model. … I have gone through a few older posts and understand the affect scaling innovations/residuals have on GARCH, but what effect does it have on the ARMA coefficients? Thanks! …

I am running an ARMA (1,1) Garch (1,1) model on some log return stock data. I am interested in backtesting this model on every day and using a rolling window of size 300. …

Here are a few of the posts I have looked through: Specifying an ARMA-GARCH model without rugarch ARMA-GARCH model selection / fit evaluation Fitting an ARCH/GARCH Model (Basics) ARMA GARCH estimation … process in practice How to fit ARMA-GARCH parameters for any distributions …

To calculate the GARCH parameters I use MLE. I assume $\sigma^2_0 = 0$. For each time $n \in [0, t]$ I march forward using the GARCH equation and the ARMA residuals until I reach $\sigma_n^2$. … I then repeat this process so that I optimize both my distribution parameters and also my GARCH parameters. …