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.

Variable Diet Plans and Net Calorie Debit Using Excel

I use a Fitbit Ultra to keep track of my daily steps, calories burned, distance traveled, etc, in conjunction with calories consumed via the Fitbit Android app. While the Fitbit website offers a few interesting ways to visualize this personal data, exporting one's data to excel opens up a virtually limitless number of options in terms of self-quantified analysis. One of the most common metrics that anyone tying to shed some pounds would be well advised to keep track of is daily net calorie consumption (or reduction). There are many factors that can contribute to how quickly one gains or loses weight (age, sex, types of calories consumed, etc), but the simple idea that you need to burn more than you consume is a fundamental concept of weight loss.

By subtracting my daily calories burned from my daily calorie intake using a simple calculation in Excel, I can visualize my calorie intake/reduction progress over extended periods in one quick glance, something the Fitbit website surprisingly doesn't happen to show on its own. By adding a weekly average to the data, I can easily see behavioral trends in this area and one interesting piece of insight I was able to infer in my case is that my net calorie debit/intake tends to cycle in ~20 day intervals. The simplest way of quantifying cycles with this particular data is done by examining the peaks and troughs of my weekly average, then summing and averaging the distance between either the peaks or troughs themselves. The result is a clear indication of a broad trend in my behavior, self-knowledge that is only apparent when seen through the the lens of Excel and cycle analysis. With knowledge such as this, a dieter may be able to create a flexible/variable (as opposed to static/unchanging) calorie intake plan that is attuned to their own personal cycles. By doing so, they may be more likely to stick to a plan that doesn't go against their natural rhythms. Additionally, one could know when to "take the foot off the gas pedal" when the cycle is peaking while also realizing when to increase exercise intensity and/or reduce calorie consumption when the cycle is bottoming, so as to achieve maximum results.

And in case anyone was wondering, the two instances on my chart where the calorie reduction exceeded 2000 for several days in a row, once near the beginning and one near the middle of the chart, represent two 5 day fasts.

Weight Graph Analysis Using TA

The attached chart is a great example of the insight financial technical analysis can bring to traditional weight charts. This particular chart plots my daily weight values in blue over the last ~11 months, and after a quick glance it becomes clear that the day to day values can be quite volatile. Two of the most common security charting techniques, the moving average and Bollinger bands, can be quite useful not only in making sense of this variability, but by also helping me keep these fluctuations in perspective. As anyone who has tracked their weight can tell you, there are times when you are doing everything right in terms of exercise and net calorie reduction, yet the pounds don't seem to come off as one might expect. This is where Bollinger bands can be useful.

Bollinger bands represent 2 standard deviations added to and subtracted from the mean, which happens to be my weekly average weight in this case (shown in orange). In a normal distribution, around 95% of the sample population is expected to fall within these values, which are represented on my chart as the grey lines above and below the daily and weekly average values. While weight values aren't technically normally distributed (or stock prices either for that matter!), the use of these bands are still quite useful in the sense that most values should still be expected to fall within this range. As my day to day weight change values begin to increase or decrease in size, the bands reflect this by widening (for an increase in volatility) and contracting (for a decrease in volatility). So when I am chugging along with my weight loss plan and the pounds are coming off quickly, the odds of a relatively dramatic subsequent increase in weight are actually increasing. This interpretation becomes clear when you look towards the beginning of my chart, when my weight was swinging widely between 185 and 195 lbs. After an initial spike up, the pounds came off just as quickly and almost to the same extent that they were added on. The tendency for weight values to behave like this is quite common, with the moving average serving as the center point of this oscillation, and I eluded to earlier, the use of moving averages on weight charts is one of the best ways to keep daily values in perspective.

Moving averages smooth data so that the short term volatility is eliminated, at the cost of some responsiveness. A moving average can be thought of as a "typical" value for the period in question, one week in my case. What is interesting about the moving average is the relationship of the daily values to the moving average itself, as the daily values tend to cluster either below or above the average and tend to stay there for similar intervals. This ebb and flow is the natural process by which we lose and gain weight, which can be comforting to someone attempting to shed some pounds. The red bar chart below my weight graph is the perfect visualization of this phenomenon. This chart, "7-day average daily weight loss", plots the cyclical nature of this process while also bringing to light the portion of time I was actually gaining weight, which is much higher than one might initially expect (during a phase were my net weight loss was pretty significant). Obviously the goal is to drop your overall weight, but the process by which this is done is fundamentally a give and take relationship: you lose some, you gain back a little less than you lost. The point is not to be discouraged by the counter-moves during the process.

What is the header chart?

The chart I've chosen to use as my blog header represents daily calories burned from around 9 and a half months of readings. By explaining the various filters I've applied to this data, we will begin to see the cool things that can be inferred about our activity levels, things that wouldn't always be readily apparent without the aid of technical analysis.

First of all, the squiggly red line represents a simple moving average of my weekly (7 day) average calories burned. Plotting a moving average allows us to remove a lot of the volatility in the day-to-day readings. If you track personal data, one of the first things you may have noticed is that the values can vary dramatically from day to day. Averaging a series of numbers over time gives us an idea of a typical reading and plotting this value moving through time tells us the direction (i.e. trend) in which that reading is moving. The use of 7 days is a natural choice since so many of our behaviors are attuned with weekly cycles. The result is a clear picture of the overall direction of (in my case) personal activity. This type of analysis can also be very useful in tracking weight since upside volatility can be very discouraging with dieters.

One thing I found interesting about this particular chart was the fact that my spikes below the weekly average (i.e. rest days) tended to rise and fall with my overall activity, when one might expect all rest days to be the same regardless of how active you were the day before. This anomaly is seen in my example, when the weekly average rises to its highest point on the chart (just under 3500), you see a series of higher high spikes but also higher low spikes. This tells me that not all rest days are created the same! As my overall activity levels are rising, I am increasingly less likely to 100% veg out on the couch, even on complete rest days.

The weekly moving average and raw calorie intake data points both oscillate around the black/red linear regression line on the chart as well, which is a mathematically generated "center trend line". The result is a line the splits the data in half and can therefore quantify basic trend direction by looking at the angle/slope. In this case, the slope is down since it moves from higher left to lower right as the chart moves through time. This was to be expected as I lost 25 lbs during the course of these readings! As I moved closer and closer to my target weight, my focus on pure calorie burning diminished.

We've only scratched the surface in terms of what we can determine from a chart like this. Cycle analysis can tell us our typical exercise or behavior intervals. Measuring data extremes vs. average values (or the relationship of 2+ averages) tells us when to expect cyclical behavioral reversals and precisely what level of activity is needed to change broad physical trends. At the very least, this chart tells me that even if I lost my tracker, 2500 calories is break-even for food consumption on even my least active days (save for Christmas at the in-laws....the lowest dip to the far right of the chart!!)

Hello world!

There are many insights that can be gained by applying methods of financial market technical analysis to self-quantified data. This type of analysis promotes increased awareness of behavioral trends and cycles, and does so for anything that the user wishes to track. From calories burned to cups of coffee consumed, charting self quantified data and applying measurements of trend, momentum, and volatility, among other measurements, will quickly become an indispensable resource for those with precise exercise related goals and those who wish to understand more about themselves and their behaviors. As for me, my name is Tucker Sferro. I am a professional commodity trader who has been using technical analysis to navigate the financial markets for over a decade now. I hold the CMT (Chartered Market Technician) license, and aim to use these skills to bring a better understanding of the nature of self quantified data.