Six weeks ago, silver appeared to be heading toward an identified area of attraction in the $17 to $19 range.
Just to recap--a state space can be reconstructed from a series of observations, by creating a scatter plot of the data lagged against itself. Key considerations are the number of dimensions (which I have limited to two for ease of presentation) and the lag. The graph above is constructed from the weekly closing price of silver, obtained from Kitco, and the lag is six weeks.
Phase space portraits often show a succession of states that are grouped together--these states may indicate the presence of an attractor, or an area of Lyapunov stability. The presence of an attractor is an indication of a system influenced by feedbacks; with negative feedbacks being responsible for confining the system to an attractor.
The behavior of a system showing more than one such attractor is normally to remain confined within one attractor until a critical threshold is surpassed, after which the system evolves rapidly to another attractor. During the transition from one attractor to another, the positive feedbacks dominate.
Here is where there can be some predictive ability. Once the system breaks free of an attractor, the expectation is that it will evolve towards another. Which one it will evolve towards can be guessed at on the basis of the trajectory.
Notice there are limitations--it will only predict things that have happened before. Consequently, you can't use this method to predict a new all-time high (or low, for that matter). Yet new all-time highs can happen (as can new all-time lows).
Sometime in April, the price-system suddenly left the area of stability ($27-$35) in which it had been confined for nearly two years. It appeared to be heading towards the area of stability in the $16-$19 range. But a funny thing happened . . .
This is an enlarged view of the $15-$30 range on a logarithmic scale. Basically, it missed the target by less than $1. Now what?
The obvious guess is that it will return to the upper attractor ($27+ on this graph). But I wouldn't be surprised if the system spent a few months filling in an attractor in the $20-$25) range. Looking on the graph at top, it looks like an obvious hole.
Just to recap--a state space can be reconstructed from a series of observations, by creating a scatter plot of the data lagged against itself. Key considerations are the number of dimensions (which I have limited to two for ease of presentation) and the lag. The graph above is constructed from the weekly closing price of silver, obtained from Kitco, and the lag is six weeks.
Phase space portraits often show a succession of states that are grouped together--these states may indicate the presence of an attractor, or an area of Lyapunov stability. The presence of an attractor is an indication of a system influenced by feedbacks; with negative feedbacks being responsible for confining the system to an attractor.
The behavior of a system showing more than one such attractor is normally to remain confined within one attractor until a critical threshold is surpassed, after which the system evolves rapidly to another attractor. During the transition from one attractor to another, the positive feedbacks dominate.
Here is where there can be some predictive ability. Once the system breaks free of an attractor, the expectation is that it will evolve towards another. Which one it will evolve towards can be guessed at on the basis of the trajectory.
Notice there are limitations--it will only predict things that have happened before. Consequently, you can't use this method to predict a new all-time high (or low, for that matter). Yet new all-time highs can happen (as can new all-time lows).
Sometime in April, the price-system suddenly left the area of stability ($27-$35) in which it had been confined for nearly two years. It appeared to be heading towards the area of stability in the $16-$19 range. But a funny thing happened . . .
This is an enlarged view of the $15-$30 range on a logarithmic scale. Basically, it missed the target by less than $1. Now what?
The obvious guess is that it will return to the upper attractor ($27+ on this graph). But I wouldn't be surprised if the system spent a few months filling in an attractor in the $20-$25) range. Looking on the graph at top, it looks like an obvious hole.
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