Crude Guidance

Linear Isosurface Equilibrium

By Steven J. Grisafi, PhD.

The Japanese Yen is overvalued, as is the USA Dollar. Applying linear isosurface equilibrium analysis, the two contributions cannot yet be fully distinguished from one another. The British Pound Sterling and the Euro Dollar are at equilibrium with respect to one another relative to the Bitcoin. The USA Dollar is either overvalued with respect to the British Pound relative to the Bitcoin or the British Pound is undervalued with respect to the USA Dollar relative to the Bitcoin. The Japanese Yen is overvalued with respect to the Euro dollar relative to the USA Dollar. This is my preliminary assessment of having applied linear isosurface equilibrium analysis to exchange rates time series data for the ¥, €, £, $ and ฿ currencies.

I have already voiced a warning regarding the use of linear isosurfaces as a poor fit to time series price data when constructing a money potential. Yet there exist further concerns that one should recognize when evaluating the results of the linear isosurface analyses. I label my assessment as crude guidance because the set of currencies I selected to evaluate are only a small subset of available currency exchanges. Also, the analyses are designed to emphasize the effect of the sovereign currencies exchange rates upon the newly devised crypto-currency, which I call the Basecoin. Upon recognizing these concerns one must then understand that evaluation of time series data used to construct a money potential depends very much upon the size of the data set used. For these analyses of the linear isosurface equilibrium I have departed from my usual procedure of utilizing a rolling data set of constant size to a growing data set as time progresses. This choice has two significant consequences, one favorable, the other unfavorable. The favorable consequence is that each datum added to the data set has decreasing influence upon all statistics evaluated from the data set. This thereby reduces volatility of all measured statistics. But because older data points are not removed from the data set as new points are introduced, historical bias within the data set can grow to become significant. We recognize that the markets we analyze are open systems such that we cannot apply ensemble averages to our data analysis. Thus we are forced always to use time series averages for which we also know that no principle of reversion to the mean exists. Hence, historical bias within a time series data set is a very real danger, but that danger must also be balanced against the need for data sets of small variance.

Although the numerical results for the equilibrium analysis change frequently, some commentary is appropriate. The ¥ versus € per $ analysis appears to suggest that the Japanese Yen is grossly overvalued with respect to the Euro Dollar relative to the USA Dollar. The data set for this analysis is very large containing over 626 data points, which suggests that historical bias would indeed be present. One need then recognize that the data set precedes Japanese Prime Minister Shinzo Abe’s anti-austerity program seeking to inflate the Japanese currency. While a straightforward time series average suggests that one should receive approximately 134 Yen for each Euro Dollar, the linear isosurface equilibrium for the same time series data set suggests one should receive about 420 Yen for each Euro Dollar. One ought not these numbers as gospel but should only recognize they indicate that the Yen is overvalued.

Compounding an overvalued Yen appears to be an overvalued USA Dollar. This conclusion is drawn from the observations that, while the Pound Sterling seems to be at equilibrium with the Euro Dollar, the USA Dollar appears to be overvalued with respect to the Pound Sterling when measured relative to the Bitcoin. A straightforward time series average suggests that one ought get 0.65£ for each USA Dollar, but the mean field equilibrium analysis suggests one should only get 0.16£ for each $. Through reciprocity one infers that the USA Dollar is overvalued with respect to the Euro Dollar. This could contribute to the apparent overvalue of the Japanese Yen with respect to the Euro Dollar since it does not necessarily follow that the Japanese Yen is overvalued with respect to the USA Dollar when measured relative to the Bitcoin. Should one seek more definitive guidance it would be necessary to analyze additional pair-wise currency markets to contrast with one another. Constructing pair-wise money potentials on linear zero contour level isosurfaces is but one tool in the methods of finance rheology.