How do we display data measured over time and identify the patterns within it?
Construct a time series plot and identify trend, seasonal, cyclic and irregular components.
How to construct a time series plot and recognise its four components, trend, seasonal, cyclic and irregular, as the starting point of any time series analysis.
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What this dot point is asking
You must construct a time series plot and identify its trend, seasonal, cyclic and irregular components.
Constructing a time series plot
A time series plot is a special scatterplot where the explanatory variable is time.
Joining the points (unlike an ordinary scatterplot) emphasises the movement over time, making patterns easier to see.
The four components
A time series is a blend of up to four components, and recognising them is the examinable skill.
A series can show several at once: monthly retail sales typically rise (trend), peak each December (seasonal), and have occasional random jumps (irregular).
Additive and multiplicative descriptions
A time series can combine its components in two ways. In an additive model the components add up, so the seasonal swing is roughly the same size each cycle regardless of the level. In a multiplicative model the components multiply, so the seasonal swing grows in proportion as the trend rises (a December lift is larger in dollars when sales are higher). On a plot, additive seasonality shows constant-height waves about the trend, while multiplicative seasonality shows waves that widen as the series climbs. Seasonal indices (which are ratios summing to the number of seasons) describe the multiplicative case, the one SCSA uses for deseasonalising.
Why identify components first
Naming the components decides the analysis that follows. A clear seasonal component means you will compute seasonal indices and deseasonalise. A clear trend means a trend line is worth fitting (after deseasonalising). Strong irregular variation suggests smoothing first. The plot is the diagnostic that tells you which tools to reach for.
Reading a plot well also guards against false conclusions: a single seasonal peak is not evidence of growth, and one irregular spike is not a change in trend. By separating the steady trend from the repeating seasonal swing and the random noise, you describe what the data is genuinely doing over time, which is the foundation for every later step of forecasting.
Exam-style practice questions
Practice questions written in the style of SCSA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
WACE 20225 marksA time series plot of monthly ice-cream sales over three years rises overall and shows a clear peak every summer and a dip every winter, with a few random spikes. (a) Identify the components present and where each shows in the description. (b) Distinguish a seasonal component from a cyclic one.Show worked answer →
Match each described feature to a named component.
(a) Trend: the overall rise over the three years. Seasonal: the summer peak and winter dip repeating each year (fixed -month period). Irregular: the random spikes. (3 marks)
(b) A seasonal component repeats over a fixed, known period (a year, a quarter); a cyclic component is a longer swing of no fixed length, such as an economic boom-and-bust cycle. (2 marks)
Markers reward correctly naming trend, seasonal and irregular from the description and the fixed-period versus variable-length distinction.
WACE 20244 marksDescribe how to construct a time series plot, and explain why time always goes on the horizontal axis.Show worked answer →
A time series plot is a scatterplot in time order, usually joined.
To construct it, plot the variable on the vertical axis against time on the horizontal axis, plotting points in chronological order and joining consecutive points with line segments to show the movement. (2 marks)
Time goes on the horizontal axis because it is the explanatory variable: the measured quantity is treated as responding to the passage of time, so reading left to right shows how the variable changes over time. (2 marks)
Markers reward the axes and joined-points construction and time as the explanatory variable.