Table P-18 contains data values that represent the monthly sales (in billions of
ID: 353182 • Letter: T
Question
Table P-18 contains data values that represent the monthly sales (in billions of dollars) of all retail stores in the United States. Using the data through 1994, perform a decomposition analysis of this series. Comment on all three components of the series. Forecast retail sales for 1995 and compare your results with the actual values provided in the table TABLE P-18 Month 1988 19891990 199I 1992 19931994 1995 January February March April May June July August 113.6 122.5 132.6 130.9 142.1 148.4 154.6 1670 115.0 89 273 28.6 143.1 145.0 155.8 164.0 131.6 141.3 148.3 149.3 154.7 164.6 184.2 192.1 130.9 139.8 145.0 48.5 159.1 170.3 181.8 187.5 136.0 150.3 154.1 159.8 165.8 176.1 187.2 2014 137.5 149.0 153.5 153.9 164.6 175.7 190.1202.6 34.1 144.6 148.9 154.6 166.0 177.7 185.8 194.9 138.7 153.0 1574 1599166.3 177.1 193.8 204.2 September 1319 144.1 145.6 46.7 160.6 1 1859 192.8 October 133.8 142.3 151 152 168.7 1764 1897 194.0 November 140.2 1488 156. 155,6 167.2 0.9 194.7 202.4 December 1710 176.5 179.70 204 218.3 233.3238.0Explanation / Answer
For decomposition analysis, Demand Dt is the function of (trend, seasonality and irregular component).
Trend is average of demand from Jan to Current month demand;
Seasonality is calculated as Demand for current month / average of trend for entire year; and then take the average of entire seasonality factor St, which will be used for Irregular component.
Irregular component is seasonality component of current month divided by seasonality component for entire year St.
Thus,calculating the same we have -
thus we have trend, seasonality and irregular component .
Using the seasonality and irregular component same for the next year and updating trend;
Forecasted demand Dt = Trend*Seasonality component 1 year back*Irregular component 1 year back, we have -
Now comparing with actual Demand, We have -
Thus model shows forecasting error <5%, which is widely accepted.
Month Actual Demand Trend Seasonality Irregular Component Jan-94 154.6 154.6 1 0.93052058 Feb-94 155.8 155.2 1.00386598 0.934117954 Mar-94 184.2 164.866667 1.11726648 1.039639451 Apr-94 181.8 169.1 1.07510349 1.000405922 May-94 187.2 172.72 1.08383511 1.008530874 Jun-94 190.1 175.616667 1.08247129 1.007261814 Jul-94 185.8 177.071429 1.04929407 0.976389727 Aug-94 193.8 179.1625 1.08169957 1.006543716 Sep-94 185.9 179.911111 1.03328804 0.96149579 Oct-94 189.7 180.89 1.04870363 0.975840312 Nov-94 194.7 182.145455 1.06892593 0.99465758 Dec-94 233.3 186.408333 1.25155349 1.164596279Related Questions
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