# One Page of Notes on a Non Linear Approach to Price Changes, from Bill Rafter

October 24, 2009 |

Much technical analysis has to do with linear calculations where the next day’s value is the result of calculating an extension of the former values: moving or exponential averages, moving linear trends, moving standard deviations. There has been so much of this that many suspect not much more juice remains in the fruit. But once you have exhausted the linear, what remains is the non-linear.

One variation of the non-linear is vector analysis, in which market movements are condensed into vectors without regard to a fixed time. Point-and-Figure analysis also “destroys” time, but acquires the constraints of blocks of price movement, and a lot of rules to go with them. Vector analysis just looks at pure movement from beginning point to one extreme, then the other extreme, and finally to the current value. If this analysis is done on end-of-day data, it has the beauty of turning the information presented as a bar into that of a flow chart. That is, end-of-day information can be transformed into intra-day data, but the process can also be used to “cut-to-the-chase” over longer time horizons. Let me illustrate.

On the left you see a stylized version of price behavior. The time period is not important, but for the purpose of illustration, let us assume that it represents the price activity within one day. The price opens, then moves to one extreme (here the high), then to the other extreme (the low), then finally to the close. These movements can be simplified by the vectors on the right. The last reported price is the arbiter as to who won and who lost. The assumption is that volume is distributed equally over the activity. The illustration also shows the calculation for the sum of the vectors, which very elegantly comes out to three times the close minus two times the midrange plus one times the open.

The sum of the vectors calculation can certainly be done on a one-day-at-a-time basis, but much more value can be gleaned if we examine it over more relevant time periods. That naturally then begs the question of which period is relevant, perhaps the most important question in this kind of work. Market followers have all sorts of favorite N values, like 50 and 200 days. However I propose that one look over the period when the positions were acquired (or when the bets were made if you prefer). Now we do not know exactly when every position was acquired, but a good estimate for the so-called “hot money” or options positions is how long it took to ramp up to the current level of open interest. This “lookback period” can be obtained by dividing the open interest level by one-half of the volume.

Let us assume that you have calculated your lookback period and it is 42 days. Then simply calculate your vectors based on the starting price 42 days ago and the movement to the high and low prices from then to the present. Each day your lookback period and extreme prices may change, and thus your sum of the vectors will change. The vector sum will move around quite a bit but a true picture will emerge if it is smoothed such as with a moving average, exponential smoother, moving trend (moving linear regression) or moving parabolic regression over the same lookback period. They all do the job and some are better than others. Here is a chart of the recent behavior of the sum of the vectors (exponentially smoothed) and the implications to trading SPX. It’s an easy way to determine when to duck.

Dr. Rafter is President of Mathematical Investment Decisions, a quantitative research consultancy