1. Quantitative Analysis for Business Lecture 9 September 6th, 2010 http://www.slideshare.net/saark/ibm401-lecture-9

2. Example I – 30 to 45 minutes Use 3-period moving average, find the seasonal indices Hint Find Moving Average Sum of seasonal indices must be equal to “n” of each cycle Deseasonalise the data

3. Example I

4. Example II – 60 minutes Using a 12-period moving average, calculate moving average for the first 2 cycles of the time series in the table. Calculate the adjusted moving average of the first 2 cycles of the time series. Using the calculated moving average and adjusted average, calculate seasonal indices for each month of the first 2 years Assuming a multiplicative model, deseasonalise the time series for the first 2 years. Using regression model Tt = 0.47t + 24.35, forecast year 4 base on multiplicative model, assume no random Calculate the forecast error using mean absolute error (MAE) and mean square error (MSE) of year 4 forecast

5. Example ii

6. solution

7. Example i Moving Average Seasonal Indices

8. Example i

9. Example i

10. Example I – Year 1 deseasonalise

11. Example I – year 2 deseasonalise

12. Example ii Using a 12-period moving average, calculate moving average for the first 2 cycles of the time series in the table. 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. The first moving average needs to be placed midway between June and July to be able to calculate the series’ moving-average

13. Example ii

14. Example ii – Seasonal indices

15. Example ii

16. Example ii Using regression model Tt = 0.47t + 24.35, forecast year 4 base on multiplicative model , assume no random F = Tt x St x Ct x Rt

17. Example ii Calculate the forecast error using mean absolute error (MAE) and mean square error (MSE) MAE = 63.31/12 = 5.28, MSE = 548.91/12 = 45.74