This provides revised plots of the prediction distributions published yesterday. The previous plots of prediction distributions should be ignored — they are not doing as advertised.
We show the prediction distribution of levels of several equity indices (plus oil price) at the end of 2011 assuming nothing happens. That is, we’ve taken out market trends and just left random drift.
While returns are approximately uncorrelated across time, that is not true of the residuals from the trend. There is significant autocorrelation in the residuals. Taking this phenomenon into account narrows the distributions to be more appetizing and more believable.
The plots are based on a revised simulation that uses blocks of 50 days. That is, for each simulated year 5 continuous blocks of length 50 are randomly selected from the standardized residuals from the garch model. With probability one-half the signs of all of the values in a block are switched — either all or none of the signs in the block are switched.
Why the error happened
Missing this would be an easy thing for a novice to do. However, the problem here was not too little knowledge but too much.
I have done a lot of garch simulations. And I know that using blocks has very little impact. But I’ve (naturally) only simulated garch models of returns. This problem is subtly different. Autopilot mode was too strong.
Figures may be reproduced with attribution.
Stock index data are from Yahoo. Oil price data are from the U. S. Energy Information Administration.
You can get the R functions that are used to create the prediction distributions with the R command:
The commands to create the prediction distribution plots are in prediction_dist.Rscript.