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Unformatted text preview: Chapter 2: Simple Descriptive Techniques Li Chen Department of Mathematics University of Bristol 1 / 44 Outline I Simple description: seasonal effect, trend, residuals I Log transformation I Analyzing trend: curve fitting, filtering, differencing I Seasonal fluctuations I Autocorrelation 2 / 44 2.1 Simple Description: (a) Seasonal Effect A verage air tem perature at R ecife, B razil, in successive m onths Y e a r Temperature (C) 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 1 9 6 2 24 25 26 27 28 3 / 44 2.1 Simple Description: (a) Seasonal Effect (Contd) I With sales and economic series there is often a seasonal effect. This may be aligned with any or more than one unit of time. I For example: electricity consumption by a town would probably show a strong daily effect and a strong seasonal effect. I The time between repeats of an effect is known as its period . I Seasonal effects are also known as cyclic . I Generally one wishes first to estimate a seasonal effect and then one can remove it to form a deseasonalized series. 4 / 44 2.1 Simple Description: (a) Seasonal Effect (Contd) D eseasonalized tem perature at R ecife T im e Temperature (C) 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 1 9 6 21.00.5 0.0 0.5 1.0 1.5 5 / 44 2.1 Simple Description: (b) Trend M onthly Totals of International A irline P assengers T im e in M o n th s Number of International Airline Passengers (in Thousands) 1 9 5 0 1 9 5 2 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 100 200 300 400 500 600 6 / 44 2.1 Simple Description: (b) Trend (Contd) I Trend can be loosely defined as longterm change in mean. I It is possible to confuse a slowly varying cyclic effect with trend and it depends on how often the series is sampled (sampling rate) and the length of the series with respect to the period of the cyclic effect. I Once again, the trend of a time series is generally estimated, recorded and then removed. 7 / 44 2.1 Simple Description: (b) Trend (Contd) M onthly Totals of International A irline P assengers T im e in M o n th s Number of International Airline Passengers (in Thousands) 1 9 5 0 1 9 5 2 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 100 200 300 400 500 600 8 / 44 2.1 Simple Description: (c) Residuals I After seasonal effects and trend has been removed the residuals may examined for any further pattern. I Generally this involves fitting various time series models to the residuals and assessing the fit. I A good model can usually help with explanation and prediction. 9 / 44 2.2 Log Transformations If there is a trend in the series and the variance increase with the mean then a log or square root transformation may be advisable to stabilize variance . M o n t h l y T o t a l s o f I n t e r n a t i o n a l A i r l i n e P a s s e n g e r s T im e in M o n th s Number of International Airline Passengers (in Thousands) 1 9 5 0 1 9 5 2 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 100 200 300 400 500 600 10 / 44 Log M onthly Totals of International A irline P assengers T im e in M o n th s Log Number of International Airline Passengers (in Thousands) 1 9 5 0 1 9 5 2 1 9 5 4 1 9 5 6 1 9 5 8 1 9 6 0 5.0 5.5 6.0 6.5 11 / 44 R esiduals of A irline D ata after Transform ing...
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This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.
 Spring '09
 jsdkasj
 Math

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