Calculating moving averages, choosing the period, centred moving averages, and plotting them to show the trend.

What this dot point is asking

AQA wants you to calculate a moving average, choose the correct period to match the seasonal pattern, understand centred moving averages, and plot moving averages to reveal the trend in a time series. The moving average is the tool that strips the seasonal wobble out of a series so the underlying trend can be seen and a trend line drawn.

What a moving average is

Because each moving average blends several consecutive readings, the seasonal highs and lows partly cancel, leaving a much smoother line that follows the trend. The trade-off is that you get fewer points than the original series (a $4$-point average over a series of length $n$ produces $n - 3$ values) and you lose detail at the very start and end.

Choosing the period

This is the most important decision. If the period matches the cycle, every average spans one complete set of seasons, so the seasonal ups and downs balance out and only the trend remains. A mismatched period (a $3$-point average on quarterly data) leaves seasonal variation in the smoothed values, defeating the purpose.

Calculating a moving average

Centred moving averages

When the period is even (such as $4$), each moving average falls between two time points rather than on one. A centred moving average fixes this by averaging two consecutive moving averages, which lines the smoothed value up with an actual time point. For example, the centred value at a quarter is the mean of the moving average just before it and the one just after it. Centring is only needed for even periods; an odd-period moving average already sits on a time point.

The moving average is the first half of the time series analysis: it produces the smoothed sequence whose trend line you draw in the forecasting topic, and from which the seasonal effects (actual value minus trend value) are then calculated. Reading a smoothed sequence is itself an exam skill: if the moving averages rise steadily, the trend is upward; if they fall, downward; if they hover around a constant, the series is roughly level. Because the moving averages strip out the seasonal swing, even a series whose raw values zig-zag dramatically can have a smooth, clearly directional set of moving averages, which is exactly the point of calculating them. Always plot the moving averages on the same axes as the raw data so the smoothing is visible.