Hi,

ARIMA-GARCH models are used to model volatility assuming a symmetric effect (if it is asymmetric TGARCH, EGARCH or GJR can be used). Usually in GARCH models we assume that the volatility is constant during the estimation period. If it is not the case, you will need to use markov switching models or a regime-switching volatility model . ARIMA in your case is used to model the mean equation. Specifying the mean equation help getting the variance accurately. Therefore, in my view, even if the volatility does not change over time, you can use ARIMA for modelling your mean equation in ARIMA-GARCH model.

Kind regards

Thushara

For example, in financial applications, the purpose is to model the mean and volatility jointly.

ARIMA - to model and forecast the first moment - return process.

GARCH - to model and forecast the second moment - volatility process.

Your question is not clear, but volatility is in somehow nonstationarity in the variance and GARCH models can be used to model this volatility... more details can be found in this attached paper:

Conference Paper An approach to forecasting QoS attributes of web services ba...

Hi

The idea of Arch-Garch is there was a high volatality for some periods of variance of risidual followed by some periids of low volatality and so.

Thus When we construct our modle (regression model or time series model) we must check The behavior of The risidual of The model and if we found altarnative behavior of volatality we do The test of homogeniaty (arch test) and if we reject null hypithesis of no arch effect, we conclude that arch famliy efect is found.

With best regard

The idea behind ARIMA-GARCH is to ensure that the linear dependence in the mean and variance is adequately captured. However, if the volatility (the supposed changing variance) of your data is constant, you need only ARIMA model given that GARCH model is useful when the variance (volatility) is not constant.

Hi

In this situstion you dont have usr Arch famlily.

Hey,

Your question is not very clear,

What exactly do you mean that your volatility is constant over time?

In fitting a volatility model to financial time series data, ARMA-GARCH model is often used when you want to fit the mean and volatility components. The ARMA model deals with the serial correlation in the return series while the ARCH/GARCH and GARCH extension are normally used to model the conditional heteroscedasticity in the data.

Loosely speaking the ARMA-GARCH-type of model is exclusively for time series data analysis. The ARMA component of the model captures and describes the systematic changes in the mean of the time series over a long period of time (trend) while, the GARCH component of the model captures and describes the systematic changes in the variance of the time series over a long period of time (volatility, i.e; the vigorous up and down movement in the time series).

No, you won’t need it

If there is not sign of volatility clustering over time, then ARIMA onlywill suffice. Do a test for serial correlation (eg Ljung Box) on the squared residuals to confirm this is so.

ARIMA/GARCH is a combination of linear ARIMA with GARCH variance. We call this the conditional mean and conditional variance model. This model can be expressed in the following mathematical expressions. The general ARIMA (r,d,m) model for the conditional mean applies to all variance models.