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# IBM401 Lecture 9

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### IBM401 Lecture 9

1. 1. Quantitative Analysis for Business<br />Lecture 9<br />September 6th, 2010<br />http://www.slideshare.net/saark/ibm401-lecture-9<br />
2. 2. Example I – 30 to 45 minutes<br />Use 3-period moving average, find the seasonal indices<br />Hint<br />Find Moving Average<br />Sum of seasonal indices must be equal to “n” of each cycle<br />Deseasonalise the data<br />
3. 3. Example I<br />
4. 4. Example II – 60 minutes<br />Using a 12-period moving average, calculate moving average for the first 2 cycles of the time series in the table. <br />Calculate the adjusted moving average of the first 2 cycles of the time series.<br />Using the calculated moving average and adjusted average, calculate seasonal indices for each month of the first 2 years<br />Assuming a multiplicative model, deseasonalise the time series for the first 2 years.<br />Using regression model Tt = 0.47t + 24.35, forecast year 4 base on multiplicative model, assume no random<br />Calculate the forecast error using mean absolute error (MAE) and mean square error (MSE) of year 4 forecast<br />
5. 5. Example ii<br />
6. 6. solution<br />
7. 7. Example i<br />Moving Average<br />Seasonal Indices<br />
8. 8. Example i<br />
9. 9. Example i<br />
10. 10. Example I – Year 1 deseasonalise<br />
11. 11. Example I – year 2 deseasonalise<br />
12. 12. Example ii<br />Using a 12-period moving average, calculate moving average for the first 2 cycles of the time series in the table.<br />With even number of periods in the moving-average cycle, we cannot directly relate the moving-average value to a period in the time series.<br />The first moving average needs to be placed midway between June and July to be able to calculate the series’ moving-average<br />
13. 13. Example ii<br />
14. 14. Example ii – Seasonal indices<br />
15. 15. Example ii<br />
16. 16. Example ii<br />Using regression model Tt = 0.47t + 24.35, forecast year 4 base on multiplicative model , assume no random<br />F = Tt x St x Ct x Rt<br />
17. 17. Example ii<br />Calculate the forecast error using mean absolute error (MAE) and mean square error (MSE)<br />MAE = 63.31/12 = 5.28, MSE = 548.91/12 = 45.74<br />