How to make a twice-differentiable function that approximates some data?

Asked Jun 05 '15 at 20:23

Active Jun 05 '15 at 22:18

Viewed 171 times

I have some time series data that I would like to approximate with a twice-differentiable function. Each time series has ~10,000 datapoints, so I definitely do not want a function that passes through all these points. This rules out using InterpolatingFunction.

I have no mathematical model for these data at all, otherwise I would use LinearModelFit or NonlinearModelFit for this.

The only solution I can think of would be to perform some type of smoothing on the data (LowpassFilter?), and then somehow generate an approximating function object from the smoothed data.

Is there a built-in function for doing this sort of thing? (It's not that I think there's anything wrong with the recipe outlined above, but as a rule I prefer to use built-in methods over home-spun ones whenever possible.)

edited Jun 05 '15 at 21:11

asked Jun 05 '15 at 20:23

kjo

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What about splines? They should work pretty well. – Grzegorz Rut Jun 05 '15 at 20:27
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did you mean to say you "do not want to pass though" all the points? – george2079 Jun 05 '15 at 20:36
@george2079: thanks! I just edited the post to add the missing "not". – kjo Jun 05 '15 at 21:12
This recent question seems related: http://mathematica.stackexchange.com/questions/85212/derivative-of-contour-in-contourplot – Michael E2 Jun 05 '15 at 21:40
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Here is a method I have used that smoothes and uses interpolation at the same time:http://mathematica.stackexchange.com/a/72037/12558 – Hugh Jun 05 '15 at 22:27
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If your datapoints are equally-spaced you can use the Savitzky-Golay filter. – Alexey Popkov Jun 08 '15 at 13:13

How to make a twice-differentiable function that approximates some data?

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