Long Term Forecasts

While our approach is mainly focused on a forecast of next week's price of WTI and the DJIA, it lends itself also to making a longer-term price forecast via simulation. The figure below shows 250 simulated sample paths of the WTI price series for 2008, using the information available up to December 2007.

Figure 1: WTI: Simulation of sample paths for 2008

The image above shows that the distribution of the WTI price one year on is right-skewed. This can also be observed for the distribution of past gross returns, and indeed one assumption of the celebrated Black-Scholes model is that future asset prices are lognormally distributed. (The lognormal distribution has a right-skewed density.)

Running many simulations leads to a point prediction (the median of the final price) and a 90% prediction interval (with the 5% and the 95% quantiles of the simulated final price as bounds):

These forecasts use information available up to, and including, December 2007. Of course they are valid only if there is no structural break before December 2008.