ARCH Modeling of Molybdenum Prices from 2013

I've compiled a time series of returns in molybdenum prices from a presentation by Roca Mines and put together an ARCH-based model to predict mol prices a few years out. The time series is a set of monthly returns ranging from 1992 to 2012, totaling around 185 observations. I'd give some utility to predictions out about 10 years but 0-5 gives less foggy results. Here's the presentation from Roca, prepared by CPM Group.

It's a simple ARCH-based model that generates a return at t as a function of the past return at t-1. The parameters of the model were tweaked by first generating 185 returns and then both minimizing residual differences between realized and generated returns numerically (a sort of chi squared) and visual comparison between generated and realized returns.

The addition that I've made is a probability-based inflationary mechanism. Mol prices go through periods of significant volatility, but it's hard to create the significant spikes such as 03-07 and in 94 so I've added a 4% probability each year for mol prices (once in 25 years) to experience an extended period of steady growth. From there, the ARCH component drives price volatility.

Here's what some individual runs and a histogram of prices outcomes at 32, 64 and 96 months look like:

Price percentiles below with format [99th, 95th, 85th, 50th, 15th, 5th, 1st].
96 months -[98.6, 52.37, 32.94, 14.58, 6.9, 4.46, 1.94]
64 months -[82.41, 45.26, 28.76, 12.14, 7.1, 5.08, 2.63]
32 months- [63.53, 35.1, 20.32, 10.5, 7.83, 6.28, 3.9]

Next step is tying those into forecasted revenue streams for some mol producers. I've compiled estimates of mol production per year for relevant mol producers. I can turn that into a monthly production number to be sold at the forecasted price and with some deductions made for cost per pound estimates, a distribution of mol profits can be had.