I recently wrote up, and submitted to the Social Science Research Network, a study of the Central England Temperature series that I did a couple of years ago and recently updated. You can access the paper at the SSRN here: A Seasonal Autoregressive Model for the Central England Temperature Series.

What I do in this analysis is build a seasonal autoregressive model for what is the longest time series of directly measured temperatures available for analysis. This model includes a linear trend component. I fit the model for both the pre-Industrial Revolution Period (1659 to 1849) and the Post-Industrial Revolution period (1949 to 1999). In the former period no trend is apparent, in the latter period I find a warming trend of 1 °C/century. This result has a borderline statistical significance (less than 3σ). I use both models to forecast the temperatures for the 21st. Century and find that the older, trend free, model does a slightly better job out-of-sample than the newer model with the trend.

 

In order to understand how Machine Learning can be applied to the problem of discovering optimal trading strategies, one has to understand how traditional analysis is applied to this topic. The basic concepts are what I'm calling Linearly Forecastable Processes and Affine Statistics. I'll start by definining a linearly forecastable process as one that may be written:

dP = α dt + σ dX.

i.e. The change in a price may be separated into a linear combination of a conditional mean, which is locally deterministic, and a stochastic part, or innovation, which is independent of the price. Now, any stochastic process may be written in this manner, since it's changes must have a mean and the distribution of changes can therefore always be conditionally centered, but — and this is important — it is not always true that the locally stochastic part is independent of the conditional mean.

An easy example of this is the discrete Markov Chain, such as that which might be used to describe a price process at high frequency. The change expressed by the conditional mean likely does not coincide with the domain the chain may occupy, and for the linear decomposition to be valid the distribution of the innovation must be contorted to deliver a change in state that does coincide the the domain the process may occupy. This constraint necessarily makes the innovation not independent of the conditional mean.

 

I am currently writing about using Machine Learning algorithms to discover Optimal Trading Rules. This work will be devided into several parts, the first of which is about developing an appropriate training set to use for the Machine Learning algorithm. I am working around an idea based on the use of Oracles in forecasting. I will put a draft of this paper on my author page at the SSRN when it is complete.  

I'm finally preparing to fully install my systems onto cloud computing platforms. This includes deleting the static IP number I have for my server rack on the farm in NJ — which may cause a little disconnectivity over the next week, but should substantially reduce maintenance going forward.  

I put the most up-to-date version in Google docs. If you follow this link you should be able to get to it. I will update this from time-to-time.  

My ancient Dell servers are decaying... odd that, since they're made of rocks and metal. I've been too busy to attend to it, but got this across to a new server a few days ago. Seems like I should do a regression of the performance of MF Global onto the dynamic trading risk factor. That will need a little work as I've moved my databases onto MySQL and there's still some teething troubles to go through.

[11/08/2011] And then squirrels ate through my power cables and I had to have the cables to the house repaired by Jersey Central Power & Light — and that work killed the cable internet which had to be redone by Comcast…