Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Saturday, September 24, 2011

Recognizing change in complex systems

"So I came downstairs and was surprised to find the dog reading the paper."

Such is the beginning of a typical shaggy dog story. If the story is true to form, the punchline would be something like the dog has been getting his news from the internet for years, or some such. If this were a true story, it would be that the dog is usually sleeping when I come downstairs. In such a case, I would presumably notice right away that the dog's behaviour was unusual.

One of the outstanding problems of complex dynamic systems is recognizing (hopefully in real time) when a change in behaviour is occurring.

Today we look at the long (ish)-term behaviour of some commodities with respect to one another. I haven't thought much about their economic significance. Today will just be arm-waving at charts, with a view to see if we can recognize the presence of change in the market fundamentals.

First up--some soft commodities. Below we see the ratio of cocoa prices to rough rice (contracts as defined in 1996).

The principal impact on the graph is from the first Ivoiran civil war. I find it interesting that the second war didn't really impact the price as much. Possibly this is because of rapidly increasing Ghanaian cocoa production. According to Voice of America, Ivoiran production is doomed due to years of under-investment.

The reconstructed phase space appears below. I have used the time delay method. To construct this figure I have smoothed the above data set through a 3-pt moving average filter, as the unfiltered data looked really noisy.

The fifteen years of data are confined to a comparatively small region of state space, with the only interesting feature the large excursion during the first civil war. This event lasted about two years. Note the magnitude, and more importantly, note the outcome--the system reverted back to the same area of phase space from which it began.

The second civil war by contrast is scarcely noticeable.

There are other ways to contruct phase space portraits. Instead of reconstructing them from a single time series we can build them from scatterplots of two (or more) time series. In studying geological systems I try to avoid this technique because it is difficult to build two time series of equivalent length and similar sample rates. For commodity time series this is less of a problem.

So let's go all out and plot the gold/copper ratio against the silver/rough rice ratio (all month-end closing prices).

IIRC, I have multiplied the silver price by 100 in the above chart. Silver and gold used $/oz, copper measured in $/lb.

Notice how for most of the fifteen year record, the states all plot within a relatively large oval (let's call this an LSA) within phase space. There have been three significant deviations from the LSA over the past fifteen years. The excursion marked A represents the strength in gold during the 2008-9 global meltdown. The excursion marked B is a rise in tandem of both silver and copper during the year 2006.

The last excursion (C) represents the recent rise in silver. This ongoing excursion appears to have lasted 17 months so far. The multi-billion dollar question is whether this is an excursion expected to revert to the  LSA, or has a bifurcation occurred, with the system evolving towards a new LSA somewhere else in phase space.

Refer once again to the phase space plot of cocoa/rough rice.

Bifurcations and excursions are both rare events. The excursions occur on at best a decadal scale. Bifurcations are more rare. Clearly they have happened in the past. For instance, the long-term gold/silver ratio was approximately 16 for centuries, but has not been near this ratio for several decades. A bifurcation occurred in the last century sometime. Perhaps we are in one now. Either way, I think it might be prudent to stock up on rice.

Disclosure: long gold, long silver, long copper, long cocoa, long rice. Sadly, I was forced to liquidate some of my cocoa holdings in the recent market turbulence.

But it was comforting.

Update (April, 2012) - I overlooked this story in the explanation for the rising price of cocoa in 2010. It seems to fit in with the first peak in the cocoa/rice ratio in 2010.

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