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If we want to calculate time varying correlation between various asset class (5 asset classes, each consisting of 10 indices) from 2005-2012 and if our purpose is not forecasting but analysis & inference based on historical data to look what the pattern is of correlation through time (constant, increase or decrease), then out of these options which one is appropriate?

  1. DCC-GARCH

  2. EWMA

  3. Historical correlations per subperiod

I possibly could use all three approaches and create various graphs, however this would create too much graphs which would make the report full of graphs, resulting in a unclear and unreadable report....

So what would the best approach be to make the report readable instead of having at least 150 graphs (5 asset classes * 3 methods * 10 indices) for all correlation coefficients?

Using approach 3, I could easily create correlation matrices per subperiod which also fixes the issue of having too much graphs. However, what should I do if I would like to use all three approaches, as for example the DCC-GARCH estimates correlation coefficients for each time t instead for a whole time period....

Any help would be appreciated...

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  • $\begingroup$ Be aware that DCC does not allow for deterministic time trends in the correlation, so it is not suited for modelling increasing or decreasing correlation over time. You can supplement the model with an extra variable, a time trend in the equation for the conditional correlation, though, but I am not sure if this option is available in the software you are using. $\endgroup$ Dec 20, 2017 at 8:22

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In general, one choose the preferred model based on a given modelling strategy. The choice of model may also depend on the required complexity for the problem at hand.

The models 1-3 are presented in the order from the most to the least complex.

  1. DCC-GARCH: The model is a very commonly applied in the econometrics literature and will most likely be deemed adequate in most empirical application. However, due to the number of assets and indices, parameter proliferation may be an issue.
  2. EWMA: A simple way of obtaining exponentially weighted correlation forecast. Will be less prone to parameter proliferation and may therefore be more practically applicable in this setting.
  3. Historical correlation per sub-period: This is a method often applied by practitioners, if they want a quick idea of the historical evolution of correlation. You will however rarely see this approach applied in top level, econometrics papers.

Chapter 4 ("Forecasting High Dimensional Covariance Matrices") in "Handbook of Volatility Models and Their Applications" is one reference for comparing the different approaches in a high-dimensional setting.

Regarding your last question, then I would say that the whole idea of studying time varying correlation is to allow for a different correlation at each point in time. For the subsampling approach, you will e.g. calculate the correlation with the last T=1000 observations and have the estimate of correlation today. This could then graphically be compared with the DCC-GARCH estimates in the same graph.

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    $\begingroup$ DCC-GARCH avoids parameter proliferation by design as there are only 3 parameters in the DCC(1,1) equation and only $1+p+q$ in a DCC(p,q) equation for the conditional correlation, regardless of the number of assets in the system. This feature (besides computational simplicity) is perhaps the reason why DCC-GARCH is so popular in high-dimensional applications. So I think your characterization of DCC-GARCH needs a revision. $\endgroup$ Dec 20, 2017 at 8:19
  • $\begingroup$ However, if everything is estimated jointly, then there are 50 GARCH models to estimate as well on top of the correlation parameters. It believe this to be somewhat tedious. However, if only bivariate systems are considered, then I would personally apply multivariate GARCH models. $\endgroup$ Dec 20, 2017 at 9:00
  • $\begingroup$ For most part, the estimation is no problem for me. The problem lies in the fact that if I would like to use at least 1 approach, it would result in at least 50 graphs.... And I honestly do not have any idea how to fix that.. 50 to 150 graphs is too much for a proper academic report, right? $\endgroup$ Dec 20, 2017 at 9:08
  • $\begingroup$ We can easily perform the estimation, but the estimation uncertainty may be very high. As I understand, then your actual problem is how to properly graph your results. I think that you can plot many of the correlation "paths" in the same figure, then apply some clever labeling. Alternatively, I would just choose some representative correlation paths to display (e.g. one for each asset pair). Again, you may choose to plot it in the same figure. $\endgroup$ Dec 20, 2017 at 9:15
  • $\begingroup$ @user3443027 and Johan, DCC typically uses stepwise estimation as the model design allows for that very naturally. First the individual GARCH models are fit, then the DCC part on top. The precise algorithm is described in the original paper by Engle. So indeed DCC is perfectly fit for high-dimensional systems. The ease of estimation is another major reason (perhaps the most important one) for why DCC is so popular. $\endgroup$ Dec 20, 2017 at 9:25

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