zerohedge.com / By The World Complex blog / 01/30/2013 17:43
Today we look at long term charts of some key commodities and investigate means by which we might gain insight into the dynamics of their price movements. The methods are from a tool-set I have used for studying climate, much of which has been presented previously.
The key problem is interpreting the dynamics of a complex system from empirical observations. These observations are in the form of measurements of some parameter, like temperature, salinity (in ocean climate studies), or price. For our purposes we will consider month-end prices of gold, silver, copper, and rough rice (CBOT contract) from January 1996 to December 2012. The copper chart appears below.
The charts are most commonly studied as a plot of price vs time. There are many articles written on the statistical methods used. Is it a cup with handle? What about that wedge at the end there? Many newsletter authors have made (or have attempted to make) a business of selling their special methods. For a limited time only*, The World Complex offers its techniques for free. At your own risk, of course.
The dynamical evolution of a complex system is described by a succession of states through which the system has evolved. We have no way of perceiving the actual state of a complex system at any given time, but we may create a “reconstructed state” from empirical observations. Ergodic theory tells us that the succession of reconstructed states will be topologically similar to the succession of actual states, so that studying the “reconstructed state space” will enable us make inferences about the dynamics of the complex system under observation.
Reconstructed states can be most easily created from multiple time series (outputs) from the system, if present, by simply presenting a scatter-plot of the corresponding observations from the different time series. They can also be constructed from a single time series, an example of which we will see next time.
Rather than drawing a best-fit line through the states, we connect them by drawing a curve through them in sequence. This curve is described as the trajectory of the system, and can be said to represent the system’s evolution through time.
The state is reconstructed in n dimensions by n observations, where n (the embedding dimension) is ideally chosen so that there are no crossings. Usually n > 3, which is a little difficult to display. Consequently, I normally use n = 2, which is less than ideal, but still useful.