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ARCH and GARCH for Volatility Forecasting and Interest Rates

Article Quant Q&A · Author: Kroll DU
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Summary

The document asks whether ARCH and GARCH models suit volatile equity markets, whether they can estimate interest rates, how forecast horizons relate to lag choice, and how to estimate model parameters by maximum likelihood. The reply clarifies that these models describe conditional volatility and are used for equity volatility analysis; interest rate levels are instead modeled with approaches such as CIR or Vasicek.

The response points readers to a paper for discussion of lag selection and likelihood estimation, but does not reproduce its method or provide empirical comparisons. It therefore offers a useful distinction between forecasting volatility and forecasting an asset’s price or interest rate, while leaving the question of optimal lags unanswered. The post also does not specify a distribution, data setup, or implementation details for fitting the models.

Key ideas

  • ARCH and GARCH model conditional volatility rather than directly forecasting prices.
  • They are used to analyze equity volatility, but that does not mean they are only appropriate in highly volatile markets.
  • Interest rate levels require a model designed for rates, such as CIR or Vasicek.
  • The document refers elsewhere for guidance on lag selection and maximum likelihood estimation.

Tags

VolatilityStatisticsEquitiesFixed income
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# Accuracy of GARCH& ARCH forecast


# Accuracy of GARCH& ARCH forecast












I'm learing ARCH&GARCH model. I have four questions that I don't know the answers

1st: ARCH & GARCH are often used to evaluate equities. Does it mean that ARCH and GARCH are fitter for high volatility market?

2nd: Can I use these two models to estimate Interest Rate market?

3rd: If yes, the accuracy of forecasting depends on lag? In another word, the longer the lag, the better of forecasting?

Ex: if lag is 1 day, I can estimate tomorrow's price by today's price. If lag is 3 day, I can estimate price in 3 day from today's price.

4th: What's the right maximum likelihood function so that I can estimate all parameters in R language?

Thanks in advance

## Answer by phdstudent (score 1, accepted)

https://quant.stackexchange.com/a/18577

Few comments on your questions:

1) Yes, Arch and Garch are suitable for equities volatility, please see: http://onlinelibrary.wiley.com/doi/10.1002/jae.800/pdf

2) No. These are models of volatility. To model interest rates use CIR, Vasicek or similar.

3) and 4) Check paper above.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.