Construct a time series plot and identify trend, seasonal, cyclic and irregular components.

What this dot point is asking

You must plot data measured over time and describe it by naming which of the four components are present.

Constructing the plot

A time series plot places time on the horizontal axis and the variable on the vertical axis, with the points joined in time order. Because time is the natural explanatory variable, the order of the points carries the meaning.

The four components

Every time series is read as a combination of up to four components.

The crucial distinction is seasonal versus cyclic: seasonal repeats over a fixed, known period (a year, a week), while cyclic swings are longer and of variable length.

Additive and multiplicative patterns

A seasonal pattern can combine with the trend in two ways. In an additive pattern the seasonal swing is roughly the same size every year, so the peaks and troughs stay a constant distance apart as the trend rises. In a multiplicative pattern the seasonal swing grows in proportion to the level, so the gap between peaks and troughs widens as the trend climbs. Recognising which one a plot shows guides whether seasonal effects are best described as fixed amounts or as fixed percentages, which connects directly to the use of seasonal indices later in the topic.

Why identifying components matters

Each component calls for a different technique. A trend is captured by smoothing or a least-squares trend line. A seasonal pattern is measured by seasonal indices and removed by deseasonalising. Irregular variation is what smoothing tries to average away. Naming the components correctly tells you which tool to reach for next, so this descriptive step is the foundation for every calculation in time series analysis.