The distributions are an attempt to see the variability if there were no market-driving news for the whole year.
Another way of thinking of it is that if someone has a prediction for the year, then moving the distribution to center on the prediction gives a sense of what results should be expected if the assumptions of the prediction are exactly right.
The green lines in the plots indicate the starting point for the year. The red lines indicate the final point. The purple lines indicate predictions from various people.
Figure 1: Dow Jones Industrial Average (USA) 2011 prediction distribution.
Figure 2: Dow Jones Industrial Average (USA) 2012 prediction distribution.
take out an (excessively volatile) expected return at each point in time
fit a GARCH(1,1) model
simulate the garch model 250 trading days ahead starting with the current state (done 5000 times)
The simulation uses 50-day blocks. 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. This is meant to work around the autocorrelation in the residuals that is induced by fitting the overly rough expected returns.
These depend on the functions defined in prediction_dist_funs2.R. Some of the functions have been revised from last year. In particular some functions have had the default for their year argument changed to 2012.
The source function can be used in R, for instance: