Monday, February 23, 2009

Temperatures update

As I've noted a couple of times, the prices on TEMP.2009.HIGH stock are very high when compared to any reasonable forecasting model. In previous posts, I used a variety of methods to forecast the 2009 temperature anomaly based only on the time series. A model using only a nonlinear time trend (year and year squared) and lagged temperature variables explains about 84% of the variation in the time series. Based on that model, it looked like there was no more than a 5% chance that 2009 would be warm enough to beat 1998.

We now have the global average temperature anomaly for January. Let's add it to the model and see what comes up.

The first way I did it was to use my model to predict January temperatures. That model provides a much worse fit than the one predicting annual temperatures, but that's to be expected. The model's predicted January temperature is spot-on: the model predicted a temperature anomaly of 0.37 and that's what we got. We would have needed an actual January temperature much higher than predicted to start me worrying about my call on this contract. Instead, I'm right on the money.

The next approach is to add January temperatures in to help predict average annual temperatures. I updated the forecasting model I previously was using to have January temperatures as an explanatory variable. I then took the regression residuals and checked how many times in the data series we've had residuals large enough that, if we had that bad a model fit this year, 2009 would beat 1998. It's happened 6 times in the 154 year series. That's 3.8%. The best fit model says we have a 3.8% chance that 2009 is warmer than 1998. Last time, we had a 7/154 chance. So, the addition of the January data makes it LESS likely that we'll beat 1998. Why is that, given that January temps are right on target? The addition of January data to the model tightens up the precision of the estimates!

Long story short, the January data suggests that the chances of 2009 beating 1998 are even lower than I'd previously thought. A fair price on this contract is $0.038.

Full disclosure: I have a very large short position on this contract, based largely on analyses like those conducted and linked to here. I'm also slightly long on the TEMP.2009 contract as my model suggests 2009 will be warmer than 2008 (74% chance), just not warm enough to beat 1998. If you want to check my work and try it for yourself, get a copy of Stata. Get the data series and import it. Add the obvious column headings. Then do the following:

gen year2 = year^2
tsset year
reg temp year year2 L1.temp L4.temp jan
predict temp_hat
predict resid, residuals
sum resid if resid > (0.543-0.3867909)

The numbers are the 1998 anomaly and the predicted 2009 anomaly. The last line will then tell you the number of times that the model has been so far out that it generated a residual sufficiently large that, if encountered again, 2009 will be warmer than 1998.

3.8%. I don't know who or what is keeping the prices up at $0.18. Current price is five times higher than it ought to be based on fundamentals.


davidinnz said...

Good analysis.

Please post this on frogblog. I predict that the price will soar, but only if the Greens are prepared to put up their own money (they have a habit of wanting to put up other people's money, eg ETS)!

Gareth said...

Sea ice price?

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