## 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:

A histogram of the residuals follows:

There was insufficient evidence to reject the null hypothesis of normal distribution. The estimated distribution of the residuals: .

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.