Trends, seasonality, and cyclicity

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Rob J. Hyndman

Professor of Statistics at Monash University

Time series patterns

Pattern Description
Trend A pattern exists involving a long-term increase OR decrease in the data
Seasonal A periodic pattern exists due to the calendar (e.g., the quarter, month, or day of the week)
Cyclic A pattern exists where the data exhibits rises and falls that are not of fixed period (duration usually of at least 2 years)
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Examples of time series patterns

ch1_vid2_aus_elec.png

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Examples of time series patterns

ch1_vid2_aus_brick.png

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Examples of time series patterns

ch1_vid2_us_treas.png

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Examples of time series patterns

ch1_vid2_lynx.png

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Seasonal or cyclic?

Differences between seasonal and cyclic patterns:

  • Seasonal pattern constant length vs. cyclic pattern variable length

  • Average length of cycle longer than length of seasonal pattern

  • Magnitude of cycle more variable than magnitude of seasonal pattern

The timing of peaks and troughs is predictable with seasonal data, but unpredictable in the long term with cyclic data.

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Let's practice!

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