Calculating a smooth 90% limit for differences in a time series

[expertalmost]

I have 50 data sets. Each set has three related time series: fast, medium, slow. My end purpose is simple, I want to generate a number that indicates a relative degree of change of the time series at each point. That relative degree of change should range between 0-1 for all the time series and all the data sets. The scales of the data set range from .0001 to 100. Attached is a spreadsheet with one data set.

To accomplish this, I calculate the differences in a time series, delta(ts)=ts(t) – ts(t-1). Now I am trying to calculate an upper limit of 90% of those deltas. In other words, draw a smooth line on those differences such that only about 10% of the differences exceed that line. I will use that 90% limit to establish a maximum to normalize the differences between 0-1. Is this the best way to do this?

I’ve been working on this for months, mostly linear programmatic methods, with no success. And trying to get it to work across 50 data sets is killing me. I’m sure there has to be an elegant mathematical way to do this. I can’t be the first guy in town trying to normalize a relative degree of change of a time series.

Any help or directions for research are greatly appreciated! Obviously my math skills are weak so examples would be most helpful. Thank you everyone for your time and brain power!

 

[mmwave]

Thank you for sharing your problem with us. Your approach of calculating the differences in the time series and then setting an upper limit is a good start. However, there are a few aspects that could be improved upon.

Firstly, instead of setting an arbitrary upper limit of 90%, it would be more accurate to use a statistical method such as the standard deviation to determine the upper limit. This would ensure that the majority of the data points fall within the limit, rather than just 90%.

Secondly, using a linear programmatic approach may not be the most effective method for this problem. Instead, you could consider using a non-linear regression model to fit a curve to the data points and then use that curve to determine the upper limit.

Lastly, it is important to consider the nature of your data sets. Are they all from the same source or do they vary in terms of their characteristics? If they are different, then it may be necessary to adjust the method accordingly for each data set.

I would also recommend consulting with a statistician or data analyst who can provide more specific guidance based on your data sets and the desired outcome. They may be able to suggest alternative methods or provide further insights.

I hope this helps and wish you the best of luck in finding a solution to your problem.