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Seasonality

Also known as: seasonal pattern, periodic pattern.

A regular pattern that repeats at a fixed period, such as higher sales every December. Without separating it, a normal seasonal rise is mistaken for growth.

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Synthetic dataExamples on this page use synthetic data created for illustration.

Definition

Seasonality is a regular pattern that repeats at a fixed period, such as higher sales every December or lower traffic every weekend. It must be separated from trend and noise, or a normal seasonal rise will be mistaken for real growth.

In plain terms

Many series have a built-in calendar: weekdays against weekends, holidays, school terms, weather. Comparing this month with last month then mixes real change with the calendar. The usual remedies are to compare with the same period a year ago (December with December) or to estimate the seasonal pattern and remove it (“seasonal adjustment”).

Seasonality can have several periods at once, such as a weekly pattern inside a yearly one, and it can change when habits or platforms change.

Example

Monthly sales index: November 100, December 140, January 95. A year earlier, December was 135.

ComparisonChangeReading
December vs November+40%Mostly the holiday season
December vs the previous December140 / 135 = +3.7%The underlying growth
January vs December−32%The post-holiday fall, not a collapse

“Sales up 40%” and “sales down 32%” in successive months both describe the calendar more than the business.

Common misunderstandings

  • “Growth from November to December is growth.” It may only be the season; compare like with like.
  • “Seasonality means yearly.” Weekly and daily cycles are just as common.
  • “Seasonal adjustment removes information.” It removes a known pattern so that other changes stand out.
  • Time Series

    Observations of one quantity recorded in time order. Neighbouring values are related and order matters, so time series need methods that respect time.

  • Moving Average

    Replacing each point of a series with the average of the points around it, to smooth short-term noise. A longer window smooths more but reacts later.

References

  1. Rob J. Hyndman, George Athanasopoulos. Forecasting: Principles and Practice, section 2.4: Time series patterns . OTexts, 2021.
  2. Rob J. Hyndman, George Athanasopoulos. Forecasting: Principles and Practice . OTexts, 2021.