## Wednesday, March 6, 2013

### Trend Efficiency and Weight Change

Perry Kaufman is a well known commodity futures trader who is recognized for his many contributions to the systematic trading space, not the least of which is an analytic tool called "Kaufman's Efficiency Ratio". This ratio measures how fluently prices change over a set period of time by taking the absolute net change in price and dividing that figure by the sum of the absolute individual incremental changes that make up the period of study. The result is a number that ranges between 0.00 and 1.00 and tells us how smooth the day to day returns are that make up the larger period in question. For example, if the price of soybean oil rose \$10.00 over the course of 1 week and happened to gain exactly \$2.00 each of the 5 weekdays that make up the trading week, the efficiency ratio would be 1.00, meaning there was absolutely no reversion in price for the period. This gives traders the ability to quickly assess (and quantify/automate) the level of trend strength or noise/consolidation for any price series, and as readers of this blog may have already come to realize, what works in financial technical analysis often works well when examining self-quantified data.

By substituting daily weight change values for securities prices in Kaufman's Efficiency Ratio, we can quantify how smoothly our process of weight gain or loss truly is. And by adding an additional twist that I like to implement, we can also show: a) the direction of weight loss for the period and b) how our weight change naturally oscillates between periods of gain and loss. Instead of taking the absolute overall change in weight as the numerator in Kaufman's Efficiency Ratio, I prefer to use my own version that takes the real change in weight. This way, instead of ranging between 0.00 and 1.00, the results can vary from -1.00 to +1.00, with negative numbers signifying weight loss and positive numbers weight gain. The attached chart shows my values using this "Two - Way Efficiency Ratio" over the last ~11 months, with a 7 day period of analysis. There are several things that one can learn by using this type of weight change analysis: 1) it becomes clear that we naturally oscillate between periods of weight loss and weight gain (this may already seem obvious to readers of this blog from previous entries), even over periods with significant weight loss, as was my case in this example 2) as the efficiency ratio approaches high levels of efficiency (i.e. nearing -1.00 or 1.00), we should begin to expect reversion to the mean, as the body takes a break from its respective expansion or contraction - note how many bars that "print" less that -0.80 that are followed by a subsequent value closer to 0.00 3) a significant portion of any weight loss program will involve volatile day-to-day weight value returns, as evidenced by the fact that the majority of readings fall somewhere between -.050 and +0.50.

As for the large block of +0.80 reading towards the right middle of the chart - disregard these as they represent about ~1 month of time where I wasn't keeping track of my weight. Fitbit makes up for missed days when exporting to excel by averaging the total weight change by the number of days missed, which is why the efficiency levels are so high in this instance.

#### 1 comment:

1. Tucker,

I wasn't aware how I could get in touch with you so I thought I would try this approach. I am completely new to fitbit and saw your comment regarding timestamps on the google docs tutorial. Is it possible for you to write a simple script that downloads a timestamp for each individual event (e.g., each step is stamped with the time it occurred)? I would be willing to pay you for your time if this is something that takes a bit to do. If it takes very little, I'd still be happy to toss a few bucks your way! :) Thanks!