Time series and moving averages
Time series and moving averages
A time series is a set of values recorded at regular intervals. Its components are the trend (long-term direction), seasonal variation (a pattern repeating within a fixed period, such as a year), and random or irregular variation. Plot the values against time and join the points; a trend line smooths the fluctuations.
Moving averages remove seasonality. For a 4-point (quarterly) series, a simple 4-point average would fall halfway between two time points, so use a centred moving average: average four consecutive values, then average consecutive pairs of those averages, and plot the result against the middle time point. This loses the first two and last two values. The seasonal component is actual value − trend value; averaging these for each quarter gives the average seasonal effect, and forecast = trend value + seasonal component.
Traps: never plot a 4-point moving average against the first or last value of the four; remember an odd-point moving average (e.g. 3-point) is already centred and needs no second averaging step; and do not forecast far beyond the data, since the trend may not continue.
Worked example. Values 10, 12, 11, 13, 14. First 4-point average = (10 + 12 + 11 + 13) ÷ 4 = 11.5. Second = (12 + 11 + 13 + 14) ÷ 4 = 12.5. Centred moving average = (11.5 + 12.5) ÷ 2 = 12.0, plotted at the third time point.