(a) Plot either receipts and outlays or federal debt and GDP (plot both time series on the same graph).

(b) Describe the trend (if any) and discuss possible causes.

(c) Fit a trend of your choice to each.

(d) Interpret each fitted trend equation, explaining its implications.

(e) To whom is this issue relevant?

U.S. Federal Finances, 2000–2011 ($ billions current)
Year	Receipts	Outlays	Federal Debt	GDP
2000	2,025	1,789	5,629	9,821
2001	1,991	1,863	5,770	10,225
2002	1,853	2,011	6,198	10,544
2003	1,782	2,160	6,760	10,980
2004	1,880	2,293	7,355	11,686
2005	2,154	2,472	7,905	12,446
2006	2,407	2,655	8,451	13,225
2007	2,568	2,729	8,951	13,892
2008	2,524	2,983	9,986	14,394
2009	2,105	3,518	11,876	14,098
2010	2,163	3,456	13,529	14,508
2011	2,174	3,819	15,476	15,080

For following fitted trend, make a prediction for period $t$ = 17:

$y_t$ = 501 + 18.2$t$ - 7.1${t}^2$

List five tips for ensuring effective forecasting outcomes.

For following fitted trend, make a prediction for period $t$ = 17:

$y_t$ = 1149 + 12.78$t$

For following fitted trend, make a prediction for period $t$ = 17:

$y_t$ = $2286e^{.076t}$

List the steps in deseasonalizing a monthly time series.

Why is seasonality irrelevant for annual data?

(a) Plot the voter participation rate.

(b) Describe the trend (if any) and discuss possible causes.

(c) Fit both a linear and a quadratic trend to the data.

(d) Which model is preferred? Why?

(e) Make a forecast for 2012, using a trend model of your choice (or a judgment forecast).

(f) If possible, check the web for the actual 2012 voter participation rate. How close was your forecast?

Note: Time is in 4-year increments, so use $t$ = 16 for the 2012 forecast.

Name an advantage and a disadvantage of each method.

Explain two ways to initialize the forecasts in an exponential smoothing process.

(a) Plot the total minutes of TV viewing time per household. (b) Describe the trend (if any) and discuss possible causes. (c) Fit a linear trend to the data. (d) Would this model give reasonable forecasts? Would another trend model be better? Explain. (e) Make a forecast for 2015. Show the forecast calculations. (f) Would these data ever approach an asymptote? Explain. Note: Time is in 5-year increments, so use t =14 for the 2015 forecast.

What does a small $\alpha$ say about the degree of smoothing? A large $\alpha$?

Interpret the smoothing constant $\alpha$. What is its range?

When is exponential smoothing most useful?