The basis of Mr. Douglas argument is to present us with two figures: one a scatterplot of gold price vs copper price; and the other a scatterplot of gold price vs silver price.

Hopefully he won't mind if I reproduce them here so we can discuss their significance.

*Copper-price vs. gold price scatterplot.*

Why this is a two-dimensional phase space for the gold and copper price.

As we have seen previously, phase spaces can be reconstructed from scatterplots of independent variables. The orthogonality of our axes may be called into question when the two time series are strongly correlated, but as long as the correlation is not perfect, we gain additional information about the system from such a plot.

The only real difference between, say, our reconstruction of the DGC share price state space and the above state space from Mr. Douglas' article is that Mr. Douglas has not joined the points in chronological order. But there is certainly enough information here to work with.

*Silver*

*-price vs. gold price scatterplot.*

Here Mr. Douglas has constructed a two-dimensional state space for the gold and silver price. Mr. Douglas has correctly pointed out that there are two groups of points each of which indicate a linear relationship between the two prices.

Mr. Douglas has performed the linear regression for us, and the result is not necessary for our critique.

The group at the left (with the black regression line) represents the gold- and silver-price states over the period from June 2003 until September 2008, whereas the right grouping represents the same over the period from September 2008 until September 2010.

Mr. Douglas asserts that the differences between these two groupings--combined with the lack of such in the gold-copper price state space--is evidence of manipulation. The World Complex will take a contrary postion--that this particular argument does not support the presence of manipulation (again we will note that World Complex agrees with Mr. Douglas that there is manipulation, but its existence is not supported by the above argument.

The principal evidence against Mr. Douglas' argument is that natural dynamic systems spontaneously develop the same structure within their state spaces. Below is a frame from a poster presented at the spring AGU conference in 2009. (abstract is the last on the list here).

The above graphs relate to acoustic characteristics of sedimentary layers in a relatively young marine basin--Emerald Basin, which lies on the Nova Scotia continental shelf. There are many difficulties in obtaining the above data, which explains its sparseness. There are also some unresolvable issues that cause unquantifiable errors, so the data are not nearly as precise as the data sets of Mr. Douglas.

As happens with Mr. Douglas graph of silver price vs gold price, some of the above units can be divided into two distinct groups each of which would have a different linear relationship. The reason that this happens relates to changes in oceanographic conditions, which effects a "reset" of the relationship between the two variables. Critically, however, the slope of the regression lines for the different groups is nearly the same (ideally the same in accurate data).

Note that the slopes of the regression lines in Mr. Douglas' gold-silver price chart are both quite similar. That slope is a defining characteristic of the relationship between the gold and silver price over the period of the plot (we would find significant changes in that slope using historical data, because that slope is 100 times the reciprocal of the gold:silver price ratio).

How do we relate our argument about natural dynamic systems to this particular economic dynamic system. Instead of changes in oceanographic conditions, we might look for any change in the economic system that happened at the point where the dynamics change. That change is apparently in September of 2008, at which time there most certainly were exciting things happening in the economic sphere.

The financial crisis that came to fruition in September 2008 may have caused the market to suddenly re-evaluate its perception of the correct relationship between the gold price and the silver price.

Is it possible to test this hypothesis?

Let's reconsider the gold-copper state space.

In this plot I have sketched in a few regression lines for groups of points on the copper-gold plot Mr. Douglas presented in his original article (actually I'm really skeptical about the little one on the far right).

I am not privy to Mr. Douglas' original time series, so I have no way of knowing whether the different groups I have indicated actually represent different intervals of time. If I were to guess, I would guess that the third line from the left starts at about September 2008, and has resulted from the same economic head-bonk that reset the gold-silver price relationship. The others in the copper -gold plot above may result from smaller economic hits, which primarily slowed the economy, affecting the copper price.

Although the World Complex disagrees with Mr. Douglas' argument in this particular case, we do agree with the manipulation of the prices of precious metals, and expect our readers to act appropriately.

(Damn--I was trying to find that huge "Buy gold" message Sprott had last year.)

## No comments:

## Post a Comment