How to determine "trendiness" of a time series I'd like to be able to compare two timeseries as to their level of "trendiness" to determine which trends better.
For example, assume two stocks, Google and IBM. Would like to understand approaches to determining which of the two trends better.
I realize that the concept of trend is a bit vague.
If one were to look at charts of two stocks (GOOG and IBM for example) one may visually exhibit smooth trends where it goes up for 20 days with little interruption and then goes down for 30 days with little interruption whereas the other may be very noisy in its movement.
Someone looking at the charts may say the first stock trends better. My question is how to mathematically/statistically determine this.
One approach might be to mark highs and lows that represent at least an N% (say 15) change in prices on both stocks and the one with the fewest N% changes therefore trends better.
Any other ideas? Is there a commonly accepted approach to this in the timeseries community?
 A: Nick Cox is correct that "trends" are the subject of a plethora of metrics by technically oriented financial analysts. While these technical trend metrics may be quite intensive methodologically, they tend to be weak or lacking in statistical rigor and motivation otherwise. In other words, they are pretty simple minded heuristics. What they do confirm is that your question is more about qualitative measures of "trendiness." On this topic there are no shortage of opinions.
My preference in trend analysis is to, first, answer the question of the growth rate and whether or not this growth is exponential or greater than exponential. The really interesting trends are the ones showing growth faster than exponential as these imply "bubbles" of some type. Then, over and against the growth rate, the slope or the rate of change in the predictors relative to Y, there is the acceleration in the slope or the rate of change in the rate of change. This is typically based on the slope of the second difference of Y wrt itself. Acceleration is also known as the Hessian and is considered one of the "greeks" in quantitative finance. Ron Gallant, in his 1986 Nonlinear Modeling book described as a good measure for the presence of nonlinearity in a time series. It has also been described as a measure of "success" or environmental fitness. I like it because acceleration gives you a quantification of the strength or magnitude of the force behind the first derivative or slope.
