# Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet.

For convenience, I've set the minimum and maximum values on the y-axis to the weights that correspond with the underweight and obese BMI cutoff values for a person of my height. The resulting graphs display some surprisingly consistent trends; a quick visual inspection of the data suggests that my weight on any given day typically differs by less than 1 kg from weights recorded on surrounding days.

I'm wondering whether there is a more precise or standard way to determine the average deviation of individual data points (from the surrounding data) in a data set whose overall trend cannot be accurately represented by any of the typical linear/exponential/power models. (I've considered splitting the data set into smaller pieces and analyzing those using regressions, but such a method seems rather inefficient and arbitrary.)

• Well, you could get the trend via local regression and compare each data point to that. But I'm not a statistician. – Rahul Apr 22 '15 at 6:34
• Cool—this certainly seems like a more precise method. I'll wait for some more responses to see if anyone else has ideas. – Rations Apr 23 '15 at 2:43

Yeah. If your data points are $x_1,x_2,\dots,x_n$, then you can compute $n-1$ new data points $y_1,y_2,\dots,y_{n-1}$ which are the differences between consecutive $x_i$s. Specifically let
$$y_i=|x_i-x_{i+1}|$$