Question 15.6: Valley Estates Quarterly House Sales Study Refer to the quar......

The four-step process to calculate the seasonal indexes is shown in Table 15.10 (steps 1 and 2), Table 15.11 (Step 3) and Table 15.12 (Step 4) respectively. Since the time series data given (house sales) is quarterly, a four-period term (k = 4) is chosen to smooth out short-term seasonal and irregular variations (since four periods span a year).

Table 15.11 shows the averaging of the seasonal ratios (Step 3) using the median as a central location measure to derive the median seasonal indexes for each quarter.

These median seasonal indexes are also called unadjusted seasonal indexes.

Finally, Table 15.12 adjusts each median seasonal index to a base of 100 (Step 4).

Management Interpretation

Each (adjusted) seasonal index measures the average magnitude of the seasonal influence on the actual values of the time series for a given period within the year. By subtracting the base index of 100 (which represents the trend/cyclical component) from each seasonal index, the extent of the influence of seasonal forces can be gauged.
For Example 15.6, the following interpretation applies:

• In quarter 1 of each year, the seasonal index of 79.1 means that, on average, Valley Estates house sales are depressed by the presence of seasonal forces by approximately 21%. Alternatively stated, house sales would be about 26% higher (\frac{21}{79}\times 100 ) had seasonal influences not been present.
• Quarter 2’s interpretation is similar to that of quarter 1, since the seasonal index is also below 100, namely 84.8.
• In quarter 3 of each year, the seasonal index of 135.2 means that, on average, Valley Estates house sales are stimulated by the presence of seasonal forces to the extent of approximately 35%. Alternatively stated, house sales would be about 35% lower had seasonal influences not been present.
• In quarter 4 of each year, seasonal influence is negligible, as the seasonal index of 100.9 is almost equal to its base index of 100, which contains only trend and cyclical measurements. Seasonal influences account for less than 1% of Valley Estates’ house sales, y, on average, in quarter 4.