„The requests remain stable“, reads a new monthly chart. In the office, however, far fewer requests came in during the most recent month. The source may still have calculated correctly: perhaps the headline refers to a moving average and not to the individual monthly figure.
The workshop is aimed at readers and editorial teams in Austria and Germany. All values are invented. They describe neither a real region nor the actual demand on any portal. Our task is to understand the point in time under consideration and the summary used.
Six months, one short peak
In the model, an office counts completed request receipts according to a consistent definition of its own. January and February each have 10, March 40, April 10, May 10 and June 10. For the purposes of the calculation, the unusual March figure is assumed to be a confirmed observation. No cause is derived from it.
Anyone who compares March and April directly sees a decline from 40 to 10, that is, by 75 per cent. This describes exactly those two monthly values. It is not yet a statement about a longer-term trend or future development.
The office now forms the mean of the most recent month and the two preceding months in each case. For March the calculation is: 10 plus 10 plus 40, divided by three, gives 20. For April it is 10 plus 40 plus 10, likewise divided by three, again 20. The moving average stays the same, although the individual monthly figure falls markedly.
What changes when the window is shifted
NIST describes moving averages as the continued averaging of smaller consecutive quantities, in which the window is shifted forward. [MA] Our own sequence of numbers shows why two identical results do not mean two similar months.
March remains within the April window. It is still included in the window for May: 40 plus 10 plus 10 gives an average of 20. Only the June window contains three 10s and gives 10. A single peak thus affects several consecutive averages.
This is a property of the stated calculation, not a hidden data error. It can be helpful when the question concerns a calmer trend. It would, however, be misleading if the smoothed value were described as the actual individual monthly figure.
Therefore disclose the window length, the method of calculation and the temporal assignment. A mean over three months is not automatically the same as a mean over a calendar quarter. After March the window in the example shifts monthly; it does not stop at January to March.
Where the value is plotted in time
The model so far assigns the mean to the last month of its window. For January, February and March it therefore sits at March. NIST additionally explains the option of placing such a mean at the centre in time for an odd-length window. [CMA]
In our three-month example, the same value of 20 would then sit at February. However, it already contains March. For a retrospective presentation, this is a different assignment; it must not be read as though this confirmed three-month value could already have been known at the end of February.
Therefore pay particular attention to the right-hand edge of a smoothed chart. Which points in time have already been calculated with a complete window? Which figures are still provisional, missing or estimated? A centred series and a continuously available trailing series do not necessarily share the same most recent point.
Smoothing is not automatically seasonal adjustment
In our model, only an average over a fixed window is formed. No recurring seasonal pattern was estimated and no calendar effect was professionally removed. The smoothed value is therefore not described as seasonally adjusted without an additional methodological account.
Averaging likewise does not correct a changed counting definition. If from April an additional type of message were counted, the comparison would first have to be clarified. A visually calm line does not make differing collection rules identical.
A genuinely missing month is also not quietly filled in as zero in the model itself. Which calculation was applied to missing values, and whether windows contain differing numbers of observations, should be found in an actual report. The calculation rule must not be guessed from the smooth trend.
Which statement belongs in the headline?
For the model case, the editorial team could place two accurate sentences side by side: „The individual monthly figure fell after the March peak. The trailing three-month average remained unchanged in April.“ This is more precise than the blanket claim that everything stayed stable.
If a chart shows only the smoothed series, its labelling should make the summary used clearly identifiable. For the specific reader question, it can be sensible to make the unaveraged values accessible alongside it. Which form is suitable remains an editorial decision according to scope and purpose.
The workshop provides no forecast. A moving average can summarise past data without reliably announcing a future turning point. The result of the reading is a more precise question: which time periods lie behind this point, where was it plotted, and what does it currently not tell us about the individual month?