Selecting GARCH Models with Forecast and Risk Evaluation

Summary

The document considers how to choose a GARCH specification for forecasting returns on a portfolio of three ETFs. It distinguishes selecting model order from assessing whether forecasts are useful. Information criteria such as AIC and BIC can help choose the number of autoregressive, moving-average, ARCH, and GARCH terms, while a multivariate GARCH package is mentioned as a possible tool for portfolio modeling.

The answers recommend comparing candidate models by out-of-sample forecast performance using loss measures such as RMSE or MAPE, or by testing forecast calibration with a Mincer–Zarnowitz regression. One-step and dynamic forecasts may also behave differently. For risk use, value-at-risk failure rates are proposed as another comparison. These checks answer different questions, so lower information criteria or forecast error alone do not demonstrate better trading or risk outcomes; the discussion offers methods but no empirical results for the ETF portfolio.

Key ideas

• AIC and BIC can guide the selection of GARCH model orders, but they do not establish forecast usefulness.
• Compare candidate specifications using forecast losses such as RMSE or MAPE.
• Mincer–Zarnowitz regression can assess whether forecasts are statistically informative.
• One-step and dynamic forecasts may yield different evaluations.
• Value-at-risk failure behavior offers a risk-focused way to compare models.

Tags

# How to find the best fitting GARCH model for a portfolio composed of 3 ETFs in R?


# How to find the best fitting GARCH model for a portfolio composed of 3 ETFs in R?












I am doing a project for my class Financial Time Series in which I am trying to forecast my portfolio log returns using a GARCH fit. I am having a bit of trouble determining the best way to fit this model, and which order model is the best fit. I have tried everything from garchM to rugarch. So far, I have gathered that the best way to determine which order is adequate, is by comparing AICs for different ordered models. If someone could please get back to me that would be great! Thanks, Jeff W

## Answer by paglos (score 1)

https://quant.stackexchange.com/a/15831

Did you try rmgarch package of R ?

http://cran.r-project.org/web/packages/rmgarch/index.html

http://unstarched.net/r-examples/rmgarch/mgarch-comparison-using-the-hong-li-misspecification-test/

## Answer by Malick (score 0)

https://quant.stackexchange.com/a/15862

I would suggest you to forecast the series using different models and to determine which one is the best accordingly loss functions such as RMSE, MAPE.. or using the Mincer-Zarnowitz regression . You could also compare one-step forecast versus dynamic forecast. Another way is to compute VaR and observe the model having the lowest failure rate. AIC/BIC criteria are useful only to select the appropriate number of AR/MA/ARCH/GARCH terms.

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