SC QUALITY GUILDTime series: moving average, trend and seasonal indices
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Enter a series in time order. Get a trailing or centered moving average, the least-squares trend and whether it is real, seasonal indices by the ratio-to-moving-average method, and a trend-times-season forecast.
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Q-BotClick for an explanation of this tool.For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
What a time series hides
Complaints, returns, scrap and demand recorded period by period usually mix several things: a long-run trend, a seasonal pattern that repeats every year (or week, or shift), longer cyclical swings, and irregular noise. Comparing this quarter with last quarter without separating them is how a team celebrates a seasonal dip or panics over a seasonal peak. Time-series analysis pulls the parts apart.
Moving averages
A moving average replaces each value with the average of a window of n consecutive values. It smooths out the noise and, when the window is exactly one season long, the seasonal pattern too, leaving the trend and cycle.
- A trailing moving average uses the latest n values. It can be updated as each period arrives, and it is a simple forecast of the next period, but it lags the data by (n − 1)/2 periods and turns late.
- A centered moving average is placed in the middle of its window, so it lines up with the data and does not lag, but it cannot be calculated at either end. With an even window (4 quarters, 12 months) the middle falls between two periods, so two adjacent averages are averaged again (a 2 × n moving average).
Trend
A least-squares line through the values against the period number gives the trend: the slope is the change per period. The p-value tests whether the slope could be zero. With strong seasonality the line is fitted to the deseasonalized values, which gives a much cleaner estimate.
Seasonal indices
The ratio-to-moving-average method (the classical multiplicative decomposition):
- compute a centered moving average one season long, which holds the trend but none of the season;
- divide each value by it, giving a ratio;
- average the ratios for each position in the season (all the first quarters, all the second quarters, and so on);
- scale the averages so they average exactly 1.
An index of 1.20 means that season runs 20% above the trend. Dividing a value by its index deseasonalizes it, so that consecutive periods can be compared fairly. Multiplying the trend by the index gives a forecast that allows for both. Some texts average the ratios with a median instead of a mean to resist outliers; this tool uses the mean.
Time series or control chart?
A control chart asks whether a process is stable. A time series with a real trend or season is not stable by definition, and a control chart of it will signal again and again. Model the trend and season first, then chart what is left over.
On the exam
The CQE Body of Knowledge asks you to define, describe and use time-series analysis, including the moving average, to identify trends and seasonal or cyclical variation (VI.E.3). The CSSBB asks you to check for seasonality effects when collecting data (V.B.4), and the CMDA asks how quantitative data reveal patterns and trends (V.C.1). Expect to compute a moving average by hand, to say how a trailing average lags, and to interpret a seasonal index.