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.
Example 1: Gold/copper vs Silver/rough rice (gold and silver as $/oz, Cu in $/lb, rice in $ per hundred-weight)
This is a plot we have looked at before. The trajectory of the system is complex and fine details are difficult to describe, but overall, the system has largely been confined to the yellow ellipse left of centre, with the exception of three periods: 1) the run-up in copper and silver prices starting in 2006; 2) the commodity collapse in late 2008, when gold held up better than the other commodities in this chart; and 3) the excursion of the past 3 years, which either started in March 2010 (orange arrow on the right at the break-out of the ellipse) or in mid 2009 (left orange arrow at the beginning of the trend). Given its size and duration, we give greater significance to the latest excursion.
But what is the nature of the excursion? Did rice collapse? Or silver rise? Silver has been rising since 2002. Then came a rapid advance up until early 2011, which I’m sure we all remember.
Same commodities–different order.
Not too different (although in this one I had rice in cents per hundredweight). Most of the past seventeen years has been spent confined to the portion of state space within the ellipse, with the exception of the three times noted in the first example, and Buffet’s purchase of silver in 1998. None of the excursions had lasting power except for the current one, which broke out of the ellipse in early 2010.
Again–did rice collapse? Or did gold suddenly accelerate in 2010?
Recombining the ratios one more time . . .
Here we see the famous “rabbit sitting in a stroller” formation, which means . . . well, you’ll have to subscribe to find out.
The main difference between this graph and the others is that there is no recent excursion of any length.
The reason is that the excursion is the separation of the precious metals (which still includes silver) from the industrial metals and agricultural commodities.
Even though gold and silver have been in a bull market for over ten years, the real regime change only happened about three years ago. What happened?
* until the powers of darkness control the internet