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 the series, identify its components, smooth or deseasonalise, fit a trend, and produce a forecast.
Components of a time series
A time series plots a variable against equally spaced time. It may show:
- Trend: a long-term upward or downward movement.
- Seasonal: a regular pattern repeating each fixed period (for example, each quarter).
- Cyclic: longer wave-like rises and falls not of fixed length.
- Irregular: random, unpredictable variation.
Moving-average smoothing
A moving average replaces each value with the mean of itself and its neighbours, smoothing out short-term fluctuations to reveal the trend. Use an odd number of points (3, 5, ...) so the average sits on an actual time point. For an even number, such as a 4-point quarterly average, you must centre it by averaging two consecutive moving averages so it aligns with a time point.
Seasonal indices
A seasonal index measures how much a season is above or below the average. The indices for one full cycle must average to (so they sum to the number of seasons). An index of means that season runs above the typical level; means below.
Fitting a trend and forecasting
Fit a least-squares line to the deseasonalised data, where numbers the time periods . To forecast, substitute the future to get the trend value, then multiply by that season's index to reseasonalise.