ch 9 - Stat 0302B Business Statistics Spring 2010-2011...

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Unformatted text preview: Stat 0302B Business Statistics Spring 2010-2011 Chapter IX Elementary Time Series and Index Numbers § 9.1 Introduction Many types of business and economic data are observations on a variable at equidistant points in time. A data set of this type is called a time series , and the variable is called a time series variable . Example 9.1 The following table shows some typical examples of time series. Time series variable Time index t Hang Seng Index ( HSI ) day Consumer Price Index ( CPI ) quarter Gross Domestic Production ( GDP ) quarter unemployment rate quarter company revenue month/year production of raw material month number of MTR passengers day number of traffic accident day activity of iodine-131 in air sample day radiation level hour Most time series are graphed and analysed so that economists and business managers can forecast the future state of the economy and of their respective businesses. P.197 Stat 0302B Business Statistics Spring 2010-2011 § 9.2 Time Series Plots A plot of the observed values of a series versus time, is the first step in any time series analysis. These time-series plots are very easy to produce by common computer software and can provide a general picture on the trend and correlation patterns. Example 9.2 1. Daily closing Hang Seng Index 2. Monthly Composite Consumer Price Index P.198 Stat 0302B Business Statistics Spring 2010-2011 3. Quarterly unemployment rate Example 9.3 Dataset: ‘ revenue.xls ’ The above dataset stores the monthly revenue (in millions of dollars) of a vehicle company from January 2008 to December 2010. P.199 Stat 0302B Business Statistics Spring 2010-2011 The time series plot can be obtained as a Line Plot of Revenue , with Month as the X-axis label. Time Series Plot of Revenues 100 200 300 400 500 600 700 800 900 1000 Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 Mar-09 May-09 Jul-09 Sep-09 Nov-09 Jan-10 Mar-10 May-10 Jul-10 Sep-10 Nov-10 Month Revenue ($million) § 9.3 Index Numbers An index number is a number that measures the change in a variable over time relative to the value of the variable during a specific base period. It can be regarded as a rescaling or standardization so that cumbersome business data can be reduced into easy understood figures. § 9.3.1 Simple Index Number A simple index number is an index based on the relative changes over time in a single variable. 100 × = y y I t t time series value at time t = t y time series value at base period = y simple index number at time t = t I The base period index number is equal to 100, i.e. 100 = I . P.200 Stat 0302B Business Statistics Spring 2010-2011 Example 9.4 Consider the revenue data in Example 9.3. If Jan-08 is taken as the base period, the index numbers of the revenue at Feb-08 and Mar-08 are calculated as Feb-08: 117 100 514 601 100 1 1 = × = × = y y I Mar-08: 162 100 514 834 100 2 2 = × = × = y y I The index numbers at the other months can be calculated similarly....
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ch 9 - Stat 0302B Business Statistics Spring 2010-2011...

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