I'm working with data that includes the returns on a financial asset and 10 other variables (for example Google-searches). My aim is to test which of these factors affect the return (not the volatility). ARMA+GARCH is the model I am supposed to use for this study.

My questions are as follows:

  1. Will the model, which I run in R, test the impact of all the variables, or do I need to test them separately?
  2. Also, is there anything I should take into account about my data? My returns are log returns, but I could use percent-returns instead.
  3. Is it possible to test with different lags?

1 Answer 1


Incorporate the extra variables and/or their lags in your conditional mean equation next to the ARMA terms.

In R you can do that by using the package "rugarch" and functions ugarchspec and ugarchfit.

  • Specify the model with ugarchspec by including these variables via the argument external.regressors within the argument mean.model.
  • Estimate the model with ugarchfit.

The reported coefficients from the conditional mean equation will tell you the effect sizes of these variables.

If you follow this, then the answers to your questions are:

  1. Yes, you will get the assessment of all variables at once.
  2. Log-returns should be fine, as they approximate percentage returns quite well as long as the percentage returns are not too far away from zero (say, up to 15%). The nice property of log-returns is that they are additive, unlike percentage returns.
  3. Yes, simply include the lags that you are interested in.
  • $\begingroup$ This is actually ARMAX model. He has exogenous variables and more interested in those coefficients. $\endgroup$ Commented Oct 27, 2017 at 12:41
  • $\begingroup$ @CagdasOzgenc, thanks, I did not realize immediately that I had phrased it in an ambiguous way. Now it should be better. $\endgroup$ Commented Oct 27, 2017 at 12:50

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