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You normalize for example by having a mean of 0 and a standard deviation of 1 for the data Use in R the scale function.


1

The point of normalization is to put everything on the same level (i dont mean price level.) Prices are usually nonstationary, so CLT doesnt apply, while returns arent. So @siegel 's answer is correct in saying use a) with return data.


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I would prefer choice a), however, I'd work with returns, not prices.


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Not sure your question is about having a process for covariance or to have multivariate GARCH. The standard viewpoint on a stochastic volatility for covariance is to use a Whishart process. See for instance Philipov, A. and M. E. Glickman (2006, July) Multivariate stochastic volatility via wishart processes. Journal of Business & Economic Statistics 24 ...


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I think you're looking for multivariate GARCH models of which this is an overview paper. Multivariate GARCH models have one big drawback: they are pretty hard to estimate due to the number of correlations. This paper by Caporin and McAleer might be of interest in that regard.



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