Trends, seasonality, and cyclicity

Forecasting in R

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)
Forecasting in R

Examples of time series patterns

ch1_vid2_aus_elec.png

Forecasting in R

Examples of time series patterns

ch1_vid2_aus_brick.png

Forecasting in R

Examples of time series patterns

ch1_vid2_us_treas.png

Forecasting in R

Examples of time series patterns

ch1_vid2_lynx.png

Forecasting in R

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.

Forecasting in R

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Forecasting in R

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