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Tutorial 12_SOLUTIONS_1 2018_22 May.pdf

# There is a strong seasonal component with first and

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There is a strong seasonal component, with first and third quarters being higher than second and fourth quarters. This is evident from the fact that every second data point is relatively high. The shapes of these ups and downs vary from year to year, indicating that there is an irregular component to these figures. As to longer term variation, for the 6 years from January 2002, there was a steady downward long-term trend. A similar trend is evident from January 2010 to the present. However, in between times there was a sharp rise: between April 2008 and January 2010, unemployment in North Carolina rose from 5.1% to 12.0%. Q12.3 “Shop and Run” sports kit store intends to measure the seasonal effect on its sales based on the last three years’ data. The seasonal indices for each q uarter of each of these three years have been provided in the table below. Use this data to calculate seasonal indices, correct to four decimal places. Year Summer Autumn Winter Spring 2013 0.9987 1.1659 1.3441 0.4926 2014 1.0046 1.1365 1.3748 0.4858 2015 1.0755 1.1246 1.2645 0.5631 Seasonal average 1.0263 1.1423 1.3278 0.5138 Sum: 1.0263+1.1423+1.3278+0.5138 = 4.0102 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 0 4 8 12 16 20 24 28 32 36 40 44 48 Time in quarters, Jan 2002 = 1 unemployment rate, North Carolina

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ETF1100 Business Statistics SOLUTIONS Tutorial 12______ 7 S1+S2+S3+S4 must be equal to 4. In this case, we need an adjustment. S1= 1.0263*4/4.0102= 1.0237 S2= 1.1423*4/4.0102= 1.1394 S3= 1.3278*4/4.0102= 1.3244 S4 =0.5138*4/4.0102 = 0.5125 Seasonal index: S1: 1.0237 S2: 1.1394 S3: 1.3244 S4: 0.5125 Q12.4 We consider further the time series of the unemployment rate in North Carolina discussed in Q12.2 above. (a) Let’s look at the period of steady decline in the unemployment rate from t = 1 (January 2002) to t = 26 (April 2008). 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 0 4 8 12 16 20 24 28 32 36 40 44 48 Time in quarters, Jan 2002 = 1 unemployment rate, North Carolina 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Jan-02 Jan-03 Jan-04 Dec-04 Dec-05 Dec-06 Dec-07 Dec-08 Unemployment rate: North Carolina
ETF1100 Business Statistics SOLUTIONS Tutorial 12______ 8 We could model this steady decline with a linear downward trend and a seasonal component. The trend line was determined based on the data from t = 1 to t = 26, using linear regression, and found to be 6.878 0.094 t T t Based on this trend line, and assuming a multiplicative model, seasonal indices were calculated and found to be: S 1 (Jan) 1.06 S 2 (Apr) 0.97 S 3 (Jul) 1.04 S 4 (Oct) 0.93 Using this trend and seasonal model, forecast the unemployment for the last two quarters of the Bush presidency (July 2008, and October 2008) and the quarter ending first month of the Obama presidency (January 2009).

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