Identifying the component of a time series in five situations

The four components. The syllabus treats a time series as made up of components, combined in an additive or a multiplicative model:

• Secular trend (T): the smooth, long-term direction of the series over many years.
• Seasonal variation (S): a regular rise and fall that repeats within a year, tied to the calendar, weather, festivals or customs.
• Cyclical variation (C): wave-like swings of boom, recession, depression and recovery lasting more than a year, as in a business cycle.
• Irregular variation (I): sudden, unforeseeable, short-lived movements caused by chance or one-off events (strikes, floods, fires, wars, policy shocks).

(i) An abrupt supply-chain disruption that halts a semiconductor plant for one month: irregular variation. It is sudden, short-lived and cannot be predicted from the past pattern of the series.

(ii) Higher online retail sales every October because of festive-season promotions: seasonal variation. The rise comes back at the same time each year and is tied to the festival calendar.

(iii) A multi-year economic boom with steadily rising consumer spending and GDP growth: cyclical variation. A boom is the upswing phase of the business cycle, lasting several years and later followed by a slowdown.

(iv) A gradual rise in average workforce productivity over a decade because of technology adoption: secular trend. It is a slow, persistent, long-run movement in one direction.

(v) A sharp drop in automotive sales in India after the US government introduced new import tariffs: irregular variation. It is a sudden fall caused by an outside, one-off policy event, not by the calendar or the business cycle. (The other reading: if the industry stayed depressed for years, some would call the later part cyclical. A long slump is cyclical only if it is part of the recurring business-cycle wave of boom, recession, depression and recovery. The question describes a sudden drop, so the answer is irregular.)

Summary.