A matter of time

R allows time series decomposition into seasonal and trend lines using in built stl() function.

The syntax is as follows:

object<-ts(object[,c],start = c(yyyy,mm,dd), freq =12)
plot(stl(object, s.window="periodic"))

where in the above example a data is monthly.
Using an arbitrary dataset I produced the following graphic.

I sought to use Mathematica to produce a similar graphic. The decomposition was relatively straightforward. The graphic formatting was the challenge (and the following results are imperfect).

It required:

  • suppression of the horizontal frame labels of all but the bottom plot
  • changing the vertical spacings of the plots in the GraphicsGrid[]
  • effect of different vertical axis ticks, particularly negative tick values displacing the plot area and leading to misalignment.
  • use of ImageResize[] to render closer resemblance to R plot

The reassuring aspect is the morphology of the seasonal component.
Some attempts at time series decomposition for the same dataset using Mathematica are presented in the following graphics:

First attempt. Note that the seasonal decomposition has not been reference to mean explaining the different scales compared with the R output.

Second attempt: seasonal component referenced to mean

Image resized. Note font distortion

A histogram of the residuals follows:

There was insufficient evidence to reject the null hypothesis of normal distribution. The estimated distribution of the residuals: \epsilon \in N(0, 1.4).

I expect that better methods could be devised and further, alternative formats that could lead to automation of plots without the need for customisation of plot vertical spacings.



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