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Dow Jones Industrial Average (DJIA)

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The data in below represent the closing value of the Dow Jones Industrial Average (DJIA) over the 29 year period from 1979 through 2007.

Year Coded Year DJIA
1979 0 838.7
1980 1 964.0
1981 2 875.0
1982 3 1046.5
1983 4 1258.6
1984 5 1211.6
1985 6 1546.7
1986 7 1896.0
1987 8 1938.8
1988 9 2168.6
1989 10 2753.2
1990 11 2633.7
1991 12 3168.8
1992 13 3301.1
1993 14 3754.1
1994 15 3834.4
1995 16 5117.1
1996 17 6448.3
1997 18 7908.3
1998 19 9181.4
1999 20 11497.1
2000 21 10788.0
2001 22 10021.5
2002 23 8341.6
2003 24 10453.9
2004 25 10788.0
2005 26 10717.5
2006 27 12463.2
2007 28 13264.8

1. When fitting a third order autoregressive model to the DJIA, what is the parameter estimate a3 for A3?
a) 0.0863
b) 0.0076
c) 0.0017

2. When testing for the significance of the third order autoregressive parameter with ? = 0.05, can A3 be deleted?
a) Yes
b) No
c) Inconclusive

3. If necessary, when fitting a second order autoregressive model to the DJIA, what is the parameter estimate a2 for A2?
a) 0.2034
b) 0.0886
c) 0.0863

4. When testing for the significance of the second?order autoregressive parameter with ? = 0.05, can A2 be deleted?
a) Yes
b) No
c) Inconclusive

5. If necessary, when fitting a first order autoregressive model to the DJIA, what is the parameter estimate a1 for A1?
a) 1.0213
b) 1.1018
c) 1.0959

6. When testing for the significance of the first order autoregressive parameter with ? = 0.05, can A1 be deleted?
a) Yes
b) No
c) Inconclusive

7. Forecast the DJIA for 2008 using the most appropriate model considered in 1) through 6).
a) 11040.1273
b) 13856.9935
c) 13879.4358.

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The solution discusses the Dow Jones Industrial Average (DJIA).

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See Also This Related BrainMass Solution

Statistics: Yearly Movie Attendance and Dow Jones Industrial

Problem 1

The following data represents the yearly movie attendance (in billions) in the United States from 1999 to 2008:

Year Attendance
1999 1.47
2000 1.42
2001 1.49
2002 1.63
2003 1.57
2004 1.53
2005 1.41
2006 1.45
2007 1.47
2008 1.55

a. Plot the time series.

b. Fit a three-year moving average to the data and plot the results.

c. Using a smoothing coefficient of W=0.50, exponentially smooth the series and plot the results.

d. Repeat (c), using W=0.25.

e. Compare the results of (c) and (d).

Problem 2

The data in the following table represents the closing values of the Dow Jones Industrial Average (DJIA) from 1979 through 2006.

Year DJIA Year DJIA
1979 838.7 1993 3754.1
1980 964.0 1994 3834.4
1981 875.0 1995 5117.1
1982 1046.5 1996 6448.3
1983 1258.6 1997 7908.3
1984 1211.6 1998 9181.4
1985 1546.7 1999 11497.1
1986 1896.0 2000 10788.0
1987 1938.8 2001 10021.5
1988 2168.6 2002 8341.6
1989 2753.2 2003 10453.9
1990 2633.7 2004 10788.0
1991 3168.8 2005 10717.5
1992 3301.1 2006 12463.2

a. Plot the data.

b. Compute a linear trend forecasting equation and plot the trend line.

c. Compute a quadratic trend forecasting equation and plot the results.

d. Compute an exponential trend forecasting equation and plot the results.

e. Which model is the most appropriate?

f. Using the most appropriate model, forecast the closing value for the DJIA in 2007. Check the accuracy of your forecast on the Internet or at your library and try to explain the difference between the forecast and the actual value.

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