Construct and interpret a time series plot, describe its features (trend, seasonality, cycles, irregular fluctuations), smooth it using moving-mean and moving-median smoothing, and fit a least-squares trend line for forecasting

What this dot point is asking

VCAA wants you to analyse data collected over time. You construct and read a time series plot, describe its features (trend, seasonality, cycles and irregular fluctuations), smooth out short-term noise with moving-mean and moving-median smoothing to reveal the underlying trend, and fit a least-squares trend line so you can forecast. This sits alongside regression as the other big bivariate technique in Data analysis.

Describing a time series

A time series plot joins data points in time order. You describe it using four features:

• Trend: a long-term upward or downward movement.
• Seasonality: a regular pattern that repeats over a fixed period, such as quarterly or monthly.
• Cycles: longer waves not tied to the calendar, such as economic booms and slumps.
• Irregular fluctuations: random, one-off variation with no pattern.

Moving-mean smoothing

For an odd window (3-point, 5-point), replace each interior point with the mean of itself and the points either side. The first and last points have no smoothed value because they lack neighbours.

Moving-median smoothing

A moving median takes the middle value of the window instead of the mean, which makes it resistant to outliers. For a 3-point median of $12, 18, 15$ you order them ($12, 15, 18$) and take $15$. Moving-median smoothing can also be done graphically straight off the plot.

Centred smoothing for an even window

A 4-point or other even-numbered moving mean lands between time points, so you centre it by taking a further 2-point mean of consecutive moving means. This realigns the smoothed value with an actual time period and is the standard way to smooth quarterly data with a 4-point mean.

Fitting a trend line and forecasting

Once a trend is clear, fit a least-squares line with time as the explanatory variable, numbering the periods $1, 2, 3, \dots$. The slope gives the average change per period, and substituting a future period number forecasts ahead. As with all regression, forecasting far beyond the data is extrapolation and unreliable.

Why this matters for the exams

Time series questions appear in most Data analysis exams and the SAC, usually asking you to smooth a short series by hand and describe the trend. The marks reward correct window alignment, the right choice of mean or median, and a description that uses the proper terms. Smoothing leads on to seasonal indices, where you quantify and remove the seasonal effect.