Today's study is based on an 18-month record of daily closing prices for Silver Wheaton Corp. (disclosure--long position)

The chart shows a pretty nice move up to the $45 range, and has since pulled back.

The double bumps near the end of the record provide enough information to define a time delay at the first minimum of the average mutual information of the time series against sequential lags. A reasonable approximation of this lag is sixteen trading days, and this lag is used in creating the phase space portrait below.

The turbulent eddies diffuse outward as share prices rise. The simplest reason is there is no inherent scale for price changes.

The graph above shows the daily change in closing price for Silver Wheaton, expressed as a percentage, over the past 18 months. There is no real trend, nor are the percentage moves larger or smaller when the price was higher. The effect of this is to produce a diffuse phase space portrait for the higher price area of the graph. Consequently, when the probability density is plotted, the areas in phase space representing higher prices will have lower probabilities than might otherwise be the case.

The simplest way to correct for this effect is to plot the reconstructed phase space on a logarithmic scale rather than a normal scale.

The bin size remains constant, which really means that the bins become larger as we move into the high-price

area of the reconstructed state space. The effect is to increase somewhat the probability density in the high-price area.

The only compelling attractors for price here are in the 17-$21 range. Like the Pelangio chart last time, this is a reflection of the amount of time spent at these price levels. The only cure is to stay at higher prices (SLW is near $35 at this writing).

Also recall that like most other technical approaches, resistance and support are due to psychological factors. For mining companies the drill can defeat technical analysis.

The chart shows a pretty nice move up to the $45 range, and has since pulled back.

The double bumps near the end of the record provide enough information to define a time delay at the first minimum of the average mutual information of the time series against sequential lags. A reasonable approximation of this lag is sixteen trading days, and this lag is used in creating the phase space portrait below.

*Share price phase space and turbulent flow*

The turbulent eddies diffuse outward as share prices rise. The simplest reason is there is no inherent scale for price changes.

The graph above shows the daily change in closing price for Silver Wheaton, expressed as a percentage, over the past 18 months. There is no real trend, nor are the percentage moves larger or smaller when the price was higher. The effect of this is to produce a diffuse phase space portrait for the higher price area of the graph. Consequently, when the probability density is plotted, the areas in phase space representing higher prices will have lower probabilities than might otherwise be the case.

The simplest way to correct for this effect is to plot the reconstructed phase space on a logarithmic scale rather than a normal scale.

The bin size remains constant, which really means that the bins become larger as we move into the high-price

area of the reconstructed state space. The effect is to increase somewhat the probability density in the high-price area.

The only compelling attractors for price here are in the 17-$21 range. Like the Pelangio chart last time, this is a reflection of the amount of time spent at these price levels. The only cure is to stay at higher prices (SLW is near $35 at this writing).

Also recall that like most other technical approaches, resistance and support are due to psychological factors. For mining companies the drill can defeat technical analysis.