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With time series data, let's say you want to model the return of the S&P 500. Could you get as good or better results by modeling each stock, and aggregating them to estimate the return of the S&P 500 instead of modeling the S&P 500 directly. Could you model the state-GDP growth of Vermont as well by modeling it at the county level (a model for each county) and then aggregating it for the State of Vermont?

There may be underlying math principles that could be relevant such as the Central Limit Theorem, and other concepts.

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  • $\begingroup$ Maybe this is of interest: nuffield.ox.ac.uk/users/hendry/HendryHubrich05.pdf $\endgroup$ – hejseb Sep 2 '15 at 19:38
  • $\begingroup$ Thank you very much, I will read this paper with much interest this evening. $\endgroup$ – Sympa Sep 2 '15 at 19:43
  • $\begingroup$ I have since read several other papers on the subject. I gather this debate is as old as the field of econometrics itself. It is also rather unresolved. Depending on the data set, one approach may supersede the other. It appears more of a matter of what is your question? If you want to understand the portfolio components dynamics it is much better to use the disaggregate approach. Otherwise, if you just want to better predict the parent-variable it can be more ambivalent. $\endgroup$ – Sympa Sep 8 '15 at 19:56
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Since no one posted an answer I figured I would answer my own question. I have since researched the subject. It appears more of a matter of what is your question? If you want to understand the portfolio component dynamics it is better to use the disaggregate approach. Otherwise, if you just want to better predict the parent-variable it can be more ambivalent. In the latter case, which is really the focus of my question, the answer is it depends on several factors. Are the disaggregate variables as easily modelable as the aggregate one? Very often, they are not. A good clue to check for that is the heteroskedasticity of such variables (Park test or Breusch-Pagan test). Often, the more heteroskedastic a variable is, the harder it is to model. Another clue is how far away are such variables from being Normally distributed (Jarques-Berra test). The further away from being Normally distributed, often the harder it is to model. Thus, model specification for the disaggregate variables can be very challenging as they are often more heteroskedastic and further away from being Normally distributed than the aggregate variable. If such is the case, the disaggregate approach will not work as well as the aggregate approach. Also, are the disaggregate variables associated with an issue of weight of such variables or mix of such variables to generate an estimate of the aggregate variable? If that is the case, the disaggregate approach has an embedded error in terms of calculating disaggregate variables mixes that will invariably differ from the actual mixes of such variables. The latter will translate into an error of the regressed estimated Mean of the aggregate variable. That is an error that is automatically erased when using the aggregate approach. Another related consideration is that if the disaggregate variables are much more volatile (higher standard deviation) and heteroskedastic (unstable variance) than the aggregate variable, this may render them more difficult to model. That's in part because they may not be so readily fit with variables such as seasonality variables and autoregressors.

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