Is there a de facto standard process or function to measure the linearity of a time series? I have Googled the problem and have come across a few different papers outlining various methods of doing this. The problem is that I'm not well-versed enough in mathematics to be able to comprehend each of these papers to determine which, if any, of these methods are best for my application.

Here are several papers that I came across:

- http://www.math.ucsd.edu/~politis/PAPER/HandbookTSA.pdf
- http://perso.ens-lyon.fr/patrick.flandrin/Hinich.pdf
- http://biomet.oxfordjournals.org/content/82/2/351.short
- http://onlinelibrary.wiley.com/doi/10.1002/for.3980050403/abstract

Just in case I phrased this incorrectly, I'll outline what I'm trying to do: I have a time series data set. I would simply like to know how much the series is like a straight line. For example, a time series derived from f(x)=2x would have a linearity of 1.0, f(x)=sin(x) would be something less, and a random data set would have a linearity of 0.0 or near-zero.

Any ideas on how to derive this measurement given an arbitrary time series?