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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

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    $\begingroup$ You cannot predict prices with ARCH/GARCH. They are models for volatility... $\endgroup$ – Slug Pue Jun 29 '15 at 20:16
  • $\begingroup$ I agree, but in these models rt is the log daily return. I can predit price by rt=ln(P(t+1)/P(t)),right? $\endgroup$ – Kroll DU Jun 29 '15 at 20:19
  • $\begingroup$ No, you start with fitting for example some ARMA model and then try to look for ARCH-effects of the residuals. I would recommend starting by looking into the basics first :) $\endgroup$ – Slug Pue Jun 29 '15 at 20:38
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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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