Is there a name for this property of a data series?
January 8, 2014 5:40 AM Subscribe
I have a series of physical data with a fairly straightforward property: it follows a path in space. If I plot a bunch of successive (x, y) values from the data, they follow a curving, looping line rather than randomly jumping all over the plot. More formally, if I have a point (x[t], y[t]) at time t and (x[t+1], y[t+1]) at time t+1, there is an upper limit on the distance between these two points (and this limit is small relative to the overall variation in the data). Is there a well-defined technical term for this property?
If the variation were random I'd call it a random walk. But it's governed by a bunch of complex physical processes that aren't relevant to the analysis I'm trying to do: the only thing I'm currently interested in is the "walk" property. Of course it's easy to give an ad-hoc formalization as I did above, but I'm sure there must be some standard terminology for this, and maybe some general results on series with these properties. I've skimmed several works on random walks and time-series analysis without finding a suitable term. I'm sure that this wheel has been invented before; what have I missed? Links and references very welcome.