How do we describe a pattern over time and use it to forecast?
Plot and describe time series, smooth with moving averages, deseasonalise with seasonal indices, fit a trend line and forecast future values.
How to identify trend, seasonal and irregular components, smooth with moving averages, compute and apply seasonal indices to deseasonalise, fit a trend line and forecast.
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What this dot point is asking
You must plot and describe a time series, smooth it, deseasonalise it, fit a trend line and forecast.
The components of a time series
A time series plots a variable against time. It blends up to four components.
Describing the series means naming which components are present and the overall direction.
Smoothing and deseasonalising
To see the trend, first reduce the noise. Moving-average smoothing averages each value with its neighbours; for quarterly data a centred four-point average removes the seasonal cycle. Seasonal indices measure each season's typical deviation from average and let you remove it.
The order matters: deseasonalise before fitting the trend (so the seasonal swing does not distort the line), and reseasonalise after forecasting (to put the season back).
Limitations of forecasts
A time-series forecast assumes the trend and seasonal pattern persist. Forecasting far beyond the data is extrapolation and is risky: trends can flatten, reverse, or be disrupted by one-off events. Always state that a forecast assumes the past pattern continues, and flag extrapolations.
Where each tool fits in the pipeline
It helps to see how the separate time-series tools connect. The time series plot identifies which components are present. Moving-average smoothing reduces noise to reveal the trend and is also used in computing seasonal indices. Seasonal indices quantify the repeating effect and let you deseasonalise. The least-squares trend line measures the genuine long-term movement of the deseasonalised data. Forecasting substitutes a future time into the trend line, and reseasonalising restores the season. Each tool is a step, and a full forecasting question moves through all of them in this order.
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 20218 marksDeseasonalised quarterly sales give a trend line , where is the first quarter of data. The Quarter 1 seasonal index is . (a) Forecast the deseasonalised sales for . (b) Reseasonalise the forecast if is a Quarter 4 with seasonal index . (c) State one limitation of this forecast.Show worked answer →
Use the trend line, then restore the season.
(a) Deseasonalised forecast at : . (3 marks)
(b) Reseasonalise by multiplying by the Quarter 4 index: , so about units. (3 marks)
(c) The forecast assumes the linear trend and seasonal pattern continue unchanged; as is beyond the data it is an extrapolation and may be unreliable. (2 marks)
Markers reward the trend substitution, multiplying by the correct season's index, and an extrapolation-based limitation.
WACE 20235 marksOutline the steps to forecast a future seasonal value from a time series, from the raw data to the final forecast.Show worked answer →
The standard pipeline runs deseasonalise, trend, reseasonalise.
Step 1: calculate the seasonal indices from the data (using averages or smoothing). Step 2: deseasonalise the data by dividing each value by its seasonal index. Step 3: fit a least-squares trend line to the deseasonalised data against a time variable . Step 4: substitute the future to forecast the deseasonalised value. Step 5: reseasonalise by multiplying by the seasonal index of the target season. (5 marks)
Markers reward all five steps in order, especially deseasonalise before fitting and reseasonalise after forecasting.