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Smoothing an irregular TimeSeries and calculate it's Derivative

Gianluigi Salvi
Posted 5 years ago

I'm not very experienced with this part of Mathematica so please bear me. I've a data set consisting of two columns, the first column is a date and the second is a numeric cumulative amount. I tried to create a time series, resample it and smooth, but I couldn't manage to smooth it enough. I'm a noob with Mathematica. Can you help me to understand what I'm doing wrong?

enter image description here

data = Import[
    "https://1drv.ms/x/s!AiF0MVfYzFaAi3cO044kGlJW0Oam?e=Mt7qTv"][[1]];

data2 = data[[2 ;;, {1, 2}]] 

DateListPlot[data2]

ts = TimeSeries[data2, 
  ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}]

tr = TimeSeriesResample[ts, "Day", 
  ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}]

MovingMap[Median, tr, Quantity[3, "Months"]]

quotient[values_, times_] := 
 First[Differences[values]/Differences[times]]

mm = 
 MovingMap[quotient[#BoundaryValues, #BoundaryTimes] &, 
  tr, {.1, Right}]


DateListPlot[mm]
POSTED BY: Gianluigi Salvi
10 Replies
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Jim Baldwin
Jim Baldwin
Posted 5 years ago

Consider the answer to the same question posted on MathematicaStackExchange which uses kernel regression.
POSTED BY: Jim Baldwin
POSTED BY: Henrik Schachner

Thanks, this is really what I was looking for
POSTED BY: Gianluigi Salvi
Mike Besso
Mike Besso
Posted 5 years ago

Thanks Henrik. I had not learned the MeanFilter[] yet. It will likely help me in my next project.
POSTED BY: Mike Besso

Here comes a simple approach using MeanFilter - I personally like this function because it preserves the values of the "x-axis" i.e. date values. Maybe this works for you (let data be your data from above):

ts = TimeSeries@data;
mfts = MeanFilter[ts, Quantity[4, "Weeks"]];
deriv0 = Differences[mfts];   (* quick and dirty method! *)
deriv1 = MeanFilter[deriv0, Quantity[4, "Weeks"]];
DateListPlot[{ts, mfts}, PlotStyle -> {Green, Red, Blue}, GridLines -> Automatic, ImageSize -> Large, PlotLabel -> "orig. values and smoothed values"]
DateListPlot[{deriv0, deriv1}, PlotStyle -> {Green, Red, Blue}, GridLines -> Automatic, ImageSize -> Large, PlotLabel -> "(deriv. of smoothed vals.) and (smoothed deriv. of smoothed vals.)"]

enter image description here
POSTED BY: Henrik Schachner 
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9EtPjmx1p+/+lj2rO"]

would work?
POSTED BY: Gianluigi Salvi

That Import gives me an empty string. Perhaps you could add the x-y pairs to the post, or put them in a notebook and attach it to the post?
POSTED BY: Daniel Lichtblau

Thanks, I will try with some different values.
POSTED BY: Gianluigi Salvi
Mike Besso
Mike Besso
Posted 5 years ago

Duke:

I've been doing a bit of resampling lately. Though, oddly enough, my use case requires the resampling method that you are using. To get smoother, I suggest you try other ResamplingMethods.

Here is what I've learned from my use case:

{"Interpolation", InterpolationOrder -> 1}

Will give you a straight line between our observation points.

{"Interpolation", InterpolationOrder -> 0}

Will give assume that the observed values remain unchanged until your next observation. This gives you a stair step curve.

As I understand it, if you increase the InterpolationOrder, then you will start using curves of the order specified as opposed to lines.

You might also want to try other "ResamplingMethods", but there is a good chance you just need to increase your InterpolationOrder.

I hope that helps.

Have a great and safe weekend.
POSTED BY: Mike Besso
Rohit Namjoshi
Rohit Namjoshi
Posted 5 years ago

Crossposted here.
POSTED BY: Rohit Namjoshi
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