Chapter4 - Chapter 4 Time Series Analysis and Index Numbers...

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Unformatted text preview: Chapter 4 Time Series Analysis and Index Numbers 2 Components of a Time Series A time series represents a variable observed across time. The time increment can be years, quarters, months, weeks, or even days. Example 4.1: The number of employees from 1997 to 2004 at Video- Example 4.1: The number of employees from 1997 to 2004 at Video- Comp recorded in the following table represents time series data. Comp recorded in the following table represents time series data. t Year Number of Employees (000s) ( Y ) 1 1997 1.1 2 1998 2.4 3 1999 4.6 4 2000 5.4 5 2001 5.9 6 2002 8.0 7 2003 9.7 8 2004 11.2 3 Components of a Time Series (cont.) The values of the time series can be presented in a table or illustrated using a scatter diagram. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 1 2 3 4 5 6 7 8 9 t Number of Employees (000s) 4 Components of a Time Series (cont.) The components of a time series are Trend ( Trend ( TR TR ) Seasonal Variation ( Seasonal Variation ( S ) Cyclical Variation ( Cyclical Variation ( C ) Irregular Activity ( Irregular Activity ( I ) The purpose of time series analysis is to describe a particular data set The purpose of time series analysis is to describe a particular data set by estimating the various components that make up this time series. by estimating the various components that make up this time series. 5 Trend ( TR ) Steady increase or decrease in the time series. Reflects any long-term growth or decline in the observations. A trend may be due to inflation, increases in the population, increases in personal income, market growth or decline, or change in technology. Usually follows a straight line (linear trend), but can also be curvilinear (quadratic trend). 6 Linear Trend In linear trend , the rate of change in Y from one time period to the next is relative constant. The linear trend line is The linear trend line is TR = TR = b b + + b b 1 t t 11.0 11.0 10.0 10.0 9.0 9.0 8.0 8.0 7.0 7.0 6.0 6.0 5.0 5.0 4.0 4.0 3.0 3.0 2.0 2.0 1.0 1.0 Number of employees (thousands) Number of employees (thousands) | 1997 1997 | 1998 1998 | 1999 1999 | 2000 2000 | 2001 2001 | 2002 2002 | 2003 2003 | 2004 2004 t Trend Line Trend Line 7 Curvilinear Trend In curvilinear trend , the time series appears to be slowing down or accelerating as time increases. For example, TR = TR = b b + + b b 1 t t + + b b 2 t t 2 represents a quadratic trend. represents a quadratic trend. Y t t b 2 < 0 < 0 (a) (a) Y t t b 2 < 0 < 0 (b) (b) Y t t b 2 > 0 > 0 (c) (c) Y t t b 2 2 > 0 > 0 (d) (d) 8 Seasonality ( S ) Seasonal variation refers to periodic increases or decreases that occur Seasonal variation refers to periodic increases or decreases that occur within a calendar year in a time series....
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Chapter4 - Chapter 4 Time Series Analysis and Index Numbers...

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