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Unformatted text preview: MN1025 Business Statistics 44 Lecture 10Friday 14/3/2008 TIME SERIES QUALITY CONTROL Reference: Lind et al. , Chapter 19 for Time Series, Chapter 17 for Quality Control. 10.1 Time series: The trend line Centred Moving Averages, which were considered in the last section, smoothed the data and helped to remove random and seasonal effects. Sometimes we need to take account of the seasonal pattern so we will show how to extract it, as well as looking at other aspects of how data vary with time. Example: Below, share prices are shown quarterly over three years. Data Display Price 610 1050 920 2040 700 1230 1060 2320 820 1410 1250 2730 The prices are graphed against time (over the 12 quarters) using STAT Time Series Time Series Plot Simple. We can see a seasonal effect (dur- ing each year) together with an underlying upward trend. In general we expect to find that the data break down as cyclical variation plus linear trend plus sea- sonal effects plus random effects . For example: temperatures rise and fall during the year, but with a gradual rise year-by-year and possibly a long-term cyclical effect. In business examples we will assume no cyclical effect. (Efforts to find a business cycle led to a figure of 7 years, early in the twentieth centurya theory now discredited.) So we look for a trend plus seasonal effects (plus some random ef- fects). Our first step will be to find the best fit line to the data, which in this context is called the trend line. We will deal with linear (i.e. straight line) trends. For example, the UK economy has grown by just over 2% per annum for the last forty years. So there is a trend line with a positive slope of just over 1.02. The trend line is the same as the line we would get if we did a linear regression of the data against time as in Lecture 8. We can also do STAT TIME SERIES TREND ANALYSIS, and in GRAPHS se- lect Display Plot, to obtain the plot below. Notice that we are also given the equation of the trend line, Price=728+95 time. In cases where the data is clustered around the trend line, the trend line and its equation can be used for prediction. For the data in our example, however, there is a strong seasonal element that we need to take into account when predicting. 10.2 Seasonal effects and prediction We now explain how to calculate the seasonal ef- fects and use these in prediction. The procedure is explained through an example: Below are the values of a set of housing units over 4 years, i.e. 16 quarters. The values are in millions of pounds. Quarter Value ( m) Year 1 1 160 2 230 3 286 4 271 Year 2 1 231 2 293 3 326 4 289 Year 3 1 236 2 291 3 324 4 296 Year 4 1 255 2 337 3 390 4 350 We plot the CMAs (centred moving averages) for the data as in the last lecture. We put the data MN1025 Business Statistics 45 in a column labeled Value and do STAT TIME SERIES MOVING AVERAGE, Variable: Value, MA length: 4, select Center the moving averages, in GRAPHS we select Plot smoothed vs. actual,in GRAPHS we select Plot smoothed vs....
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