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See the thread "What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?": in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned in the thread "Does ARIMA require normally distributed errors or normally distributed input data?".

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model (i.e. two-stage estimation) won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

As pointed out in the comments, fitting both models simultaneously is better than fitting one and then the other. I haven't done this personaly with R, but there is a package called rugarch might have this functionality. There's a writeup at the author's blog.

See the thread "What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?": in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned in the thread "Does ARIMA require normally distributed errors or normally distributed input data?".

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model (i.e. two-stage estimation) won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

As pointed out in the comments, fitting both models simultaneously is better than fitting one and then the other. I haven't done this personaly with R, but there is a package called rugarch might have this functionality. There's a writeup at the author's blog.

See here: in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned here.

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model (i.e. two-stage estimation) won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

As pointed out in the comments, fitting both models simultaneously is better than fitting one and then the other. I haven't done this personaly with R, but there is a package called rugarch might have this functionality. There's a writeup at the author's blog.

See the thread "What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?": in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned in the thread "Does ARIMA require normally distributed errors or normally distributed input data?".

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model (i.e. two-stage estimation) won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

As pointed out in the comments, fitting both models simultaneously is better than fitting one and then the other. I haven't done this personaly with R, but there is a package called rugarch might have this functionality. There's a writeup at the author's blog.

See here: in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned here.

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

There's also an R package called rugarch that has a lot of nice functionality built in. There's a writeup at the author's blog.

See here: in general, the error process only needs to be homoskedastic over time.

If the model was fitted with a Gaussian likelihood, you do need to assume normal residuals to conduct parametric inference, as mentioned here.

It's been a while since I've studied ARIMA in detail, but I suspect that heavy-tailed residuals will cause the same kinds of inference problems for ARIMA that they cause for other regression models that assume normality.

Since you don't say anything about heteroskedasticity, I'm assuming you don't have any. In that case, there's not much GARCH will do for you. GARCH models the change in variance over time, but there's no change to model.

As for modeling in R, "analysis" is a broad word. If you mean that you want to generate predictions, note that adding a GARCH model on top of your ARIMA model (i.e. two-stage estimation) won't change your forecasts; but if you want to, say, generate confidence bands around your prediction, you can use the GARCH predictions as the standard errors.

As pointed out in the comments, fitting both models simultaneously is better than fitting one and then the other. I haven't done this personaly with R, but there is a package called rugarch might have this functionality. There's a writeup at the author's blog.