Features of a time series

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What this lesson covers

  • The trend is the long-run direction.
  • Seasonality repeats at a fixed period.
  • An additive model is data = trend + seasonal + residual.
Key idea

The parts

  • Trend: the overall movement, up, down or flat.
  • Seasonal: a pattern repeating every year or week.
  • Residual: what is left over.
  • Outliers: unusual values with a reason worth finding.
Worked example

Reading a series

  • Quarterly sales for Kōwhai Café, a made-up example.
QuarterQ1Q2Q3Q4
Year 140605070
Year 248685878
Worked example

What it shows

  • Compare the same quarter across the years.
  1. Each quarter rises by 8 in a yearan upward trend
  2. Q4 is always highest and Q1 lowesta seasonal pattern

Common mistakes

  • Comparing Q1 with Q2 to judge the trend.
    Seasons get in the way, so compare the same quarter.
  • Describing the graph with no context.
    Use the units and the real meaning.

Your turn

  • 1. A series rises every December and drops each January. Which feature is that?
  • 2. Why compare Q1 with last year's Q1?
Show answer

1. A seasonal pattern 2. It removes the seasonal effect

Summary

What to take away

  • Trend, seasonal, residual.
  • Always write in context.

More in AS 91580

Features of a time seriesNotesMoving averages and the trendNotesSeasonal effects and forecastingNotesReporting on a time seriesNotes

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