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

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

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?

(a) Plot both Swiss watch time series on the same graph.

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

(c) Fit an exponential trend to each time series.

(d) Interpret each fitted trend carefully. What conclusion do you draw?

(e) Make forecasts for the next 3 years, using the linear trend model. Why might 2009 have been unusual? Explain.

When is a cen- tered moving average harder to calculate?

Name two types of moving averages.

When do we use a moving average?