Time Series Moving Averages

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Presentation transcript:

Time Series Moving Averages GCSE Statistics Time Series Moving Averages

Time series may show large variations Time series may show large variations . This can make it difficult to see the trend of the data and draw a trend line A moving average is an average worked out over a given number of successive observations the number of points in each moving average should cover one complete cycle of seasons. So if the data is quarterly you find the average for 4 points (numbers) of data if there are 5 readings a season you calculate a 5-point moving average (Monday – Friday UK) if there are 6 readings a season you calculate a 6-point moving average (bi-monthly) if there are 7 readings a season you calculate a 7-point moving average (7 days in a week) Higher students can expect to deal with up seven-point moving averages

Calculate a 4-point moving average for this data. Accident and health insurance premiums paid in the Netherlands in millions of euros. 1st quarter 2nd quarter 3rd quarter 4th quarter 1997 43 17 15 1998 47 19 18 1999 57 26 22 13 Calculate a 4-point moving average for this data. (watch the yellow boxes find the mean of each set of four moving along the data) 1997 1998 1999 1 2 3 4 43 17 15 47 19 18 57 26 22 13 22.5 23.5 24 24.75 25.5 28 29.75 30.75 29.5 17+15+15+47 4 43+17+15+15 4 15+15+47+19 4

Yes I put this twice in the hope you remember it! Moving averages are plotted on the time series graph to help show the trend The are plotted at the midpoint of the time interval they cover which is why the table on the last slide is set up the way it is. The points that are plotted for moving averages should not be joined up Yes I put this twice in the hope you remember it! There needs to be a key on your graph x for the observations and for the moving averages, say if they are 4 point, or 6 point or 7 point.

You can draw a trend line through the moving averages by eye The trend line is a straight line with roughly equal number of points above and below the line DO NOT JOIN THE DOTS It will be more accurate as a measure of trend than one drawn using the original data (If the trend is level the line will go through the points) Check out example 5 and example 6 on page 220-221

Your Turn exercise 6E page 223 Stuck or mathematically confused ? pgarnett@alsson.com