Question 15.3: Fire Insurance Claims Study Refer to the problem scenario of......
Fire Insurance Claims Study
Refer to the problem scenario of Example 15.2 and the time series data set in Table 15.2.
Management Question
Calculate and graph the three-period and five-period moving average series for the number of fire insurance claims. Compare the two moving average series.
Table 15.2 Number of fire insurance claims received by an insurance company (2008–2011)
| 2008 | 2009 | 2010 | 2011 | |||||||||
| Period | P1 | P2 | P3 | P1 | P2 | P3 | P1 | P2 | P3 | P1 | P2 | P3 |
| Claims (y) | 7 | 3 | 5 | 9 | 7 | 9 | 12 | 4 | 10 | 13 | 9 | 10 |
Table 15.4 shows both the three-period and five-period moving average values of fire insurance claims received.
Figure 15.6 is a line plot of the original y-values, and both the three-period and fiveperiod moving average value of the time series of fire insurance claims received. It highlights the effect of different terms (k = 3 and then k = 5) on the smoothing process.
From a comparison of the line plots of the three-period and five-period moving average values, it can be seen that there is less fluctuation (greater smoothing) in the five-period moving average series than in the three-period moving average series.
Table 15.4 Three-period and five-period moving averages of fire insurance claims received
| Period | Claims (y) | Three-period moving average | Five-period moving total | Five-period moving average |
| 2008 P1 | 7 | — | — | — |
| P2 | 3 | 5.00 | — | — |
| P3 | 5 | 5.67 | 31 | 6.2 |
| 2009 P1 | 9 | 7.00 | 33 | 6.6 |
| P2 | 7 | 8.33 | 42 | 8.4 |
| P3 | 9 | 9.33 | 41 | 8.2 |
| 2010 P1 | 12 | 8.33 | 42 | 8.4 |
| P2 | 4 | 8.67 | 48 | 9.6 |
| P3 | 10 | 9.00 | 48 | 9.6 |
| 2011 P1 | 13 | 10.67 | 46 | 9.2 |
| P2 | 9 | 10.67 | — | — |
| P3 | 10 | — | — | — |
