Time Series - Bringing it together

Taxes collected by the Westminster City government were modeled with quarterly data over the past ten years. Taxes included sales, use and property taxes. The trend equation for this quarterly data is noted below. The 1st quarter 10 years ago was coded 1, 2nd quarter was coded 2 and so forth to 40 (10 years x 4). Taxes collected was measured in millions of dollars (eg, 10,000,000 was recorded as a 10)

Trend equation Y' = 5 X + 10 The quarterly seasonal indices are noted in the table below.

Qtr 1 2 3 4

Seasonal Index 120 or 1.20 | 110 or 1.10 | 90 or .90 | 80 or .80

1. What is the average growth in taxes collected over the past 10 years. __________
2. What is the estimated deseasonalized taxes collected for year 11 for each of its four quarters. 1.__________, 2. __________ 3. ___________ 4. _________
3. This forecast in question #2 from above includes what components of the time series model, (Trend, Cyclical, Seasonal, Error) _____________
4. What is the estimated seasonally adjusted taxes that will be collected in each quarter of the 11th year. 1. ________, 2. _________ 3. ____________ 4. _________

1 2 3 4

Trend Estimate 215 | 220 | 225 | 230

Seasonals 1.20 | 1.10 | 0.90 | 0.80

Seas x Tax Est 258 | 242 | 202.5 | 184

5. Suppose the 11th year taxes (year immediately coming up) were expected to be under trend (line) by 2 percent. You believe this to be the case because of a softening in retail sales and use taxes collected in the last two quarters in the current year and an expected decrease in home valuations based on recent selling prices of homes. What would the expected taxes collected be for quarters 1 and 2 of the 11th year after adjustment for the cyclical softening? 1. ________, 2. _________