1. If you are using exponential smoothing for forecasting an annual time series of revenues, what is your forecast for next year if the smoothed value for this year is $32.4 million?

2. Consider a nine-year moving average used to smooth a time series that was first recorded in 1984.

a. Which year serves as the first centered value in the smoothed series?

b. How many years of values in the series are lost when computing all the nine-year moving averages?

3. You are using exponential smoothing on an annual time series concerning total revenues (in $millions). You decide to use a smoothing coefficient of W = 0.20, and the exponentially smoothed value for 2013 is E2013 = (0.20)(12.1) + (0.80)(9.4).

a. What is the smoothed value of this series in 2013?

b. What is the smoothed value of this series in 2014 if the value of the series in that year is $11.5 million?

4. If you are using the method of least squares for fitting trends in an annual time series containing 25 consecutive yearly values,

a. What coded value do you assign to X for the first year in the series?

b. What coded value do you assign to X for the fifth year in the series?

c. What coded value do you assign to X for the most recent re-corded year in the series?

d. What coded value do you assign to X if you want to project the trend and make a forecast five years beyond the last observed value?

5. The linear trend forecasting equation for an annual time series containing 22 values (from 1992 to 2013) on total revenues (in $millions) is

Yi = 4.0 + 1.5Xi a. Interpret the Y intercept, b0.

b. Interpret the slope, b1.

c. What is the fitted trend value for the fifth year?

d. What is the fitted trend value for the most recent year?

e. What is the projected trend forecast three years after the last value?