Polar Plots, from Jim Sogi

October 31, 2008 |

 Winter surf is starting up. Surf prediction is almost as important, (to me) as stock prediction. One of the tools for surf prediction are polar plots of wind and swell direction from the offshore buoys. A few years back Chair mentioned polar coordinates and plots. These can be done in R. I thought a simple plot of the direction and angle of market price might be helpful in some models to predict. For waves, NOAA uses data from offshore data buoys and says:

Spectra and source term are presented for selected output locations in the form of polar plots. The radial lines in the polar plots depict the directional resolution of the model. The concentric circles are plotted at 0.05 Hz intervals, where the innermost circle corresponds to 0.05 Hz and the outermost circle corresponds to 0.25 Hz. Wave energy plotted in the lower left quadrant travels in SW directions etc. The blue arrow in the center of the plots depicts wind speed and direction. Colors represent wave energy density for spectra and rates of change of energy density for source terms and are plotted at a logarithmic scale where the contours separating the colors increase by a factor of 2.

This application might be good for markets as a different sort of plot on the question, "Is the market going up or down, and how fast?". Surf direction and speed is critical to choose the spot, and equipment. Market direction and intensity is critical, but hard to predict. Surf travels generally from north to south in the winter. Market forces generally tend to travel East to West. Perhaps a polar plot of the prevailing market winds, and the concentrations of energy might be helpful in predicting market direction and intensity.

Jeff Watson writes:

As a serious student of surf prediction, I note and live by the seasonality of the swells. Different seasons bring swells from different directions, and Sogi-San is lucky to live in a place that gets swell from all 360 degrees, ensuring year round surf somewhere in the islands. Surf prediction is easy at my location as we have roughly two primary causes of swell; Cold fronts and hurricanes. We only have a window of roughly 90 degrees where conditions will produce rideable waves I check our weather maps daily and look at all the buoy information from the NOAA, whether it's surf season or not. From my location it is pretty easy to predict when we will get swells, although predicting the size gets rather tricky. To predict the size takes a lot of experience, comparisons of past data, and a firm grasp of current weather conditions…much like looking at the markets. Although it's anecdotal, I find it much easier to predict the possibility of waves than future market action.

One thing of note, sometimes mysto swells will appear out of nowhere, lasting only a very short time, with no apparent cause, disappearing as quickly as they arrive much to the chagrin of the locals. The swells that hit with no warning cause a lot of surfers to miss out on waves, because they aren't positioned to hit the swell. The markets do the same thing with movements that come out of nowhere, surprising the participants who are out of position, causing the players to be frantic while trying to catch the move which is usually missed. All of this, whether with the waves or markets, sometimes comes with no valid explanation. When I talk to groms about the waves and swell, I sometimes resort to using the cliche, "It is what it is." The same thing can be said about market moves.

Vinh Tu adds:

Mathematically, angles are even closer to correlations. Two series of t observations can be represented as two vectors in t-dimensional space. You get the cosine from dividing the dot product of the two series by the volatility of each series.

I'm not sure whether, with more than two instruments, you can still flatten it to a circle and still have it show anything useful. But restricting the plot to two series, we could take one series to be "North" –logical candidates for this might be an interest rate, or a "market portfolio", or a major market index. Then the other series could be examined in relation to North. Samples of the other series could be colour coded and assigned polar positions.

Alternatively, perhaps north could be a straight line representing a desired or hypothesized drift. The result would be somewhat related to the R-squared technical trend indicator.

Alex Castaldo quibbles:

A correlation is exactly like the cosine of an angle, as opposed to an angle.  Because cosine is an even function, there is an ambiguity as to the sign of the angle.  For example if Bonds represent North and Stocks are correlated 0.5 with Bonds, how should that be plotted? As +60 degrees (approx. W-N-W) or -60 degrees (approx E-N-E)?


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