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We can take the variance series and apply ARIMA model on it to have forecasting of volatility.

"ARIMA modelling is not the best in this circumstance because it models the mean rather than the variance. Therefore ARCH modelling is preferable"

What does this mean?

Richard Hardy
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Hola
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1 Answers1

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If the series of conditional variances were observable, you could apply ARIMA on it. However, conditional variances are not observable, so you use (G)ARCH.

Regarding the quote, check out "What is the difference between GARCH and ARMA?". We have more than one good answer there.

Richard Hardy
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  • Thanks for the prompt answer. +1. – User1865345 Nov 09 '22 at 11:12
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    @User1865345, you are welcome! And thanks for the suggestion! – Richard Hardy Nov 09 '22 at 11:13
  • Hi, could you please tell what do we mean by "since variance is not observed". Variance can be calculated using individual daily returns using the standard variance formula. Thanks for help! – Hola Nov 10 '22 at 03:59
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    @Hola, we observe realizations of random variables like $x_t$ but not the parameters like $\sigma_t$. Yes, we can easily estimate the unconditional variance $\sigma^2$ from a data sample of size $T$ if we assume independence of observations. However, we cannot estimate the conditional variances $\sigma_t$ without an assumption amounting to GARCH, as there are as many conditional variances as there are observations ($T$ of each). And we can estimate ARIMA using $x_1,\dots,x_T$ which are observed but not using $\sigma_1,\dots,\sigma_T$ which are not observable. – Richard Hardy Nov 10 '22 at 05:55
  • Thank you very much @RichardHardy for clearing my doubts. – Hola Nov 10 '22 at 08:34