Question 15.7: De-seasonalised Valley Estates Quarterly House Sales Study R......
De-seasonalised Valley Estates Quarterly House Sales Study
Refer to the house sales time series data shown in Table 15.9. The sales director of Valley Estates would like to observe the general direction of house sales without the effect of short-term seasonal influences.
Management Question
Derive a de-seasonalised time series of the quarterly house sales for the sales director of Valley Estates for the period 2008 to 2011. Use the seasonal indexes from Table 15.12.
Table 15.9 Quarterly house sales by Valley Estates (2008–2011)
| Quarter | 2008 | 2009 | 2010 | 2011 |
| Q1 | 54 | 55 | 49 | 60 |
| Q2 | 58 | 61 | 55 | 64 |
| Q3 | 94 | 87 | 95 | 99 |
| Q4 | 70 | 66 | 74 | 80 |
Table 15.12 Valley Estate house sales – adjusted seasonal indexes (Step 4)
Adjustment factor = \frac{400}{402.43} = 0.994
| Period | Median seasonal index | Adjustment factor | Adjusted seasonal index |
| Quarter 1 | 79.57 | 0.994 | 79.1 |
| Quarter 2 | 85.33 | 0.994 | 84.8 |
| Quarter 3 | 135.99 | 0.994 | 135.2 |
| Quarter 4 | 101.54 | 0.994 | 100.9 |
| Total | 402.43 | 400 |
Table 15.13 shows the de-seasonalised house sales, while Figure 15.8 shows the plot of the two line graphs (actual house sales versus de-seasonalised house sales).
Management Interpretation
Quarter 1 2008 house sales, for example, would have been higher at 68 units instead of the actual sales of 54 units had seasonal influences not been present. Similarly, house sales for quarter 3 2009, would have been lower at 64 units instead of the actual sales of 87 units had seasonal influences not been present.
In addition, the de-seasonalised quarterly house sales line graph for Valley Estates shows a very modest growth over the past four years.
Table 15.13 De-seasonalised house sales for Valley Estates and plots
| Period | House sales | Seasonal index | De-seasonalised house sales |
| 2008 Q1 | 54 | 79.1 | 68.3 |
| Q2 | 58 | 84.8 | 68.4 |
| Q3 | 94 | 135.2 | 69.5 |
| Q4 | 70 | 100.9 | 69.4 |
| 2009 Q1 | 55 | 79.1 | 69.5 |
| Q2 | 61 | 84.8 | 71.9 |
| Q3 | 87 | 135.2 | 64.3 |
| Q4 | 66 | 100.9 | 65.4 |
| 2010 Q1 | 49 | 79.1 | 61.9 |
| Q2 | 55 | 84.8 | 64.9 |
| Q3 | 95 | 135.2 | 70.3 |
| Q4 | 74 | 100.9 | 73.3 |
| 2011 Q1 | 60 | 79.1 | 75.9 |
| Q2 | 64 | 84.8 | 75.5 |
| Q3 | 99 | 135.2 | 73.2 |
| Q4 | 80 | 100.9 | 79.3 |
