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I'm trying to analyse the South African mutual fund industry returns over the last 40 years (since January 1980), however due to data limitations I was only able to obtain the monthly returns going back as far as 2005.

My hope is to use some type of model to extend the series back to 1980. I obtained the monthly stock market index returns going back to January 1980 and was thinking of using a regression model, but after applying fitting such a model, I found that the residuals of the model (and indeed the mutual fund returns themselves) displays heteroscedasticity (which was confirmed through performing an Engle arch test).

The summary statistics of the regression show the the model is statistically significant (with the p-value of the F-test being essentially zero and R Square of 92%), but I know that heteroscedasticity will tend of overstate the significance of such a test.

My question then is, can I still use the regression model or will that be a bad idea? Is there perhaps an alternative model that I could use?

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  • $\begingroup$ Why not just aggregate your monthly returns and do annual numbers back to 1980 rather than by month. I am not sure how you are doing regression here, serial autocorrelation would be one of many problems. $\endgroup$
    – user54285
    Commented Nov 12, 2020 at 22:07
  • $\begingroup$ Thanks @user54285 - do you have suggestions for any other type of model? $\endgroup$ Commented Nov 14, 2020 at 5:57

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Are you just trying to forecast. Or explain the variables? If just forecasting try exponential smoothing which have a good track record and are robust to violations of methods. If trying to explain variables none of the options are easy to do. You have to start by seeing if autocorrelation exists and there are more serious issues than that. The simplest time series regression, if you want to explain a variable, is probably ARDL or regression with ARIMA error but there are many others. I would get a book on time series regression first (I have read many and still am not brave enough to try this).:) Unfortunately I have yet to find a good introductory time series book despite a lot of looking.

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  • $\begingroup$ Thanks. I'm just trying to forecast - so I will definitely try the exponential smoothing. I'm also not brave enough to try one of those explanatory models :) $\endgroup$ Commented Nov 18, 2020 at 8:49
  • $\begingroup$ It is the simplest. You may want to look at the R smooth module, although it has a lot of esm types I have never heard of and its not easy to identify the classical esm like winters from that. $\endgroup$
    – user54285
    Commented Nov 18, 2020 at 16:38
  • $\begingroup$ Great, will do - thanks again for the help! $\endgroup$ Commented Nov 20, 2020 at 8:44

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