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# Time-Series Forecasting

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16.7 The following data (stored in Treasury) represent the three-month Treasury bill rates in the U.S. from 1991-2008:
Year Rate
1991 5.38
1992 3.43
1993 3.00
1994 4.25
1995 5.49
1996 5.01
1997 5.06
1998 4.78
1999 4.64
2000 5.82
2001 3.40
2002 1.61
2003 1.01
2004 1.37
2005 3.15
2006 4.73
2007 4.36
2008 1.37

a. Plot the data.
b. Fit a 3-yar moving average to the data and plot the results.
c. Using a smooth coeffiecient of W- 0.50, expenentially smooth the series and plot the results.
d. What is your exponentially smoothed forecast for 2009?
e. Repeat (c) and (d), using a smoothing coefficient of w= 0.25.
f. Compare the results of (d) and (e).

16.13 GDP is a major indcator of a nation's overall economic activity. It consists of personal consumption expenditures, gross domestic investment, net exports of goods and services, and government consumption expenditures. The GDP (in billions of current dollars) for the US fro 1980-2008 is stored in GDP.
a. Plot the data.
b. Compute a linear trend forecasting equation and plot the trend line.
c. What are your forecasts for 2009 and 2010?
d. What conclusions can you reach concerning the trend in GDP?

16.15 The data in Strategic represent the amount of oil, in billions of barrel, helf in the US strategic oil reserve, from 1981-2008.
a. Plot the data.
b. Compute a linear trend forecasting equation and plot the results.
c. Compute a quadratic trend forecasting equation and plot the results.
d. Compute an expoential trend forecasting equation and plot the results.
e. Which model is most appropriate?
f. Using the most appropriate model, forecast the number of barrels, in billions, for 2009. Check how accurate your forecast is by locating the true value for 2009 on the internet or in your library.

16.47 The following data (stored in Credit) are monthly credit card charges (in millions of dollars) for a populat credic card issued by a large bank.
Month 2007 2008 2009
January 31.9 39.4 45.0
February 27.0 36.2 39.6
March 31.3 40.5
April 31.0 44.6
May 39.4 46.8
June 40.7 44.7
July 42.3 52.2
August 49.5 54.0
September 45.0 48.8
October 50.0 55.8
November 50.9 58.7
December 58.5 63.4

a. Compute the time-series plot.
b. Describe the monthly pattern that is evident in the data.
c. In general, would you say that the overall dollar amounts charged on the bank's credit cards is increasing or decreasing? Explain.
d. Note that Dec 2008 charges were more than \$63 million, but those for Feb 2009 were less than \$40 million. Was Feb's total close to what you would have expected?
e. Develop an exponential trend forecasting equation w/ monthly components.
f. Interpret the monthly compound growth rate.
g. Interpret the Jan multiplier.
h. What is the predicated value for Mar 2009?
i. What is the predicated value for Apr 2009?
j. How can this type of time-series forecasting benefit the bank?