Which of the following methods to measure seasonal variations comparatively…

Concept: Methods for measuring seasonal variation differ in how completely each one uses the given time series. A method that builds an average or fits a trend using the whole series at once (a plain average across cycles, a single fitted trend line, or a relative computed against just the one adjacent period) can produce a result for almost every period. A method that instead needs a genuine moving window of neighboring periods before it can produce a comparable value cannot produce that value for the periods too close to either end of the series, because there are not enough neighbors on one side.

Here, the ratio-to-moving-average method first computes a moving average centered at each period. A centered moving average of a given span needs an equal number of periods on both sides, so it cannot be computed for a block of periods at the very start and the very end of the series - those periods are left without a moving-average value and so without a seasonal ratio at all. This structurally excludes more of the given data than the other three approaches.

• Simple average method: averages every value recorded for a given season across all cycles in the series, so no period is excluded.

• Ratio-to-trend method: a single trend line is fitted to the entire series, and every period then gets a ratio to its own trend value, so no period is excluded.

• Link relative method: each period's relative is computed against only the immediately preceding period, so only the very first period in the series is left without a relative.

• Ratio-to-moving-average method: a moving average can only be centered where there are enough neighboring periods on both sides, so a whole block of periods is left out at each end of the series before a ratio can even be computed.

Hence, the ratio-to-moving-average method is the one that comparatively utilizes the given data the least.