Context: I have a couple of series of data, stock index data. I translate those distributions into two input stream for a videogame, and let the input compete. One of the two is definitively more efficient than the other (more than 50% more), and I wanted to prove or disprove that the most efficient series is due to it's spikyness (being the winner more spiky). With spiky I mean the opposite of smooth: I don't know the statistical term for this qualifier, but it probably is affected by the difference between a point and the near points (since a smooth line has no big difference between near values)
My objective: Generate a series similar (meaning: same average, std deviation, and autocorrelation) to an already existent series, with fixed range [0, 1].
In particular, one of my original series is the following:
Standard Deviation: 0,1831
To generate a randomized series that shares these values, these are my steps:
- I generate a linear series with given average. (Purple line, gr 2)
- I generate, every 50 elements, a random variation from that curve. I vary from a random number between -0,2 and 0,2, that is a completely arbitrary number, chosen by trial and error. (Blue line, gr 2)
- Same procedure, but every element and with a step of -0,021 and 0,021. (Final result, as shown in the first graph, gr 3)
Average: 0,3572 (Similar enough)
Standard Deviation: 0,2351 (A bit off)
Auto-correlation: 0,02314 (Pretty good)
Bounds: [0, 0,8175] (A bit off)
I am not completely satisfied with the result. The values are there and they are similar enough, but the shapes of the two series are different for my purpose: my generated series seems to change more prominently "point-by-point", and it definitely looks more spiky. Is this the best method to achieve the result? Is autocorrelation a good qualifier for "spikyness"?
Note on the autocorrelation: I am using Excel for calculation, generation and plotting, and what I calculate is the derivative point by point of the original distribution, and the Standard Deviation of the newly-obtained distribution is the auto-correlation. Is it the right/fastest way to proceed?