Moving averages
In a time series, random fluctuations can usually be treated as noise that can obscure trend and other signal in the series. Various smoothing methods have been proposed to reduce these random fluctuations and show the systematic movement in the series more clearly. These methods replace each value in the series with a function of it and the adjacent values.
smoothed value = centre ( original value and adjacent values )
For example, each value might be replaced by the mean of it and the two adjacent values, replacing the value at time i by
This smoothed fit is called a 3-point moving average. Moving averages are also called running means. Greater smoothing is obtained with means of more adjacent values. For example, a 7-point moving average replaces each value with the mean of it and the 3 adjacent values on each side.
Ends of the series
Moving averages are effective at highlighting the trend in the centre of a time series, but cannot be used at the ends since the moving average requires values both before and after each value being smoothed. As the amount of smoothing increases, the number of unsmoothed values at the ends of the series also increases. For example, if 7-point moving averages are used, 3 values at each end of the series cannot be smoothed.
Southern Oscillation
The Southern Oscillation Index is defined as the barometric pressure difference between Tahiti and the Darwin Islands at sea level. The southern oscillation is a predictor of El Nino which in turn is thought to be a driver of world-wide weather. Specifically, repeated southern oscillation values less than -1 typically defines an El Nino. The time series plot shows the index between January 1984 and December 1992.
Click the arrows to adjust the number of adjacent values used to smooth the series. Click on any data point on the graph to display the raw and smoothed values. Observe that...
Click on any point on the graph to highlight the adjacent values that are used in finding the moving average at that time.