So, it̵;s really shocking how easy this should be, vs how little information there is out there on the topic. Basically I have some slightly noisy but generally exponential data, and I̵;m running a $y=a*e{-bx} $ regression on it. Thats the easy part. Hard part is that the customer wants to know the interval it might fall between over time. I’m thinking like one of those election forecast graphs where the interval starts at the CI at the last available data, then diverges more over time. However, all the articles I’ve found use feature based (looking at the variance in features to guess the PI, but in time series the variance in x is small and constant, so no good) and not only that, but when I implement them they don’t so much as meet the CI of the plot. The data clearly varies well outside the interval.

The approach I’ve done on my own isn’t exactly rigorous but does show some promising results is to run bootstrapping and then take the statistics of the parameters of the models and pick some standard deviation off the mean for those parameters. There are a full 360 degrees of possible plots this way, however, given there are 2 parameters. I also doubt it’s empirical integrity, but I’ll admit the solution does look valid.

Any advice?

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