Chapter 11 Times Series 483
c. Insert a trend line smoothing the
batting average using a ten-year
moving average.
d. Calculate the ACF and state your con-
clusions (notice that the ACF does
not drop off to zero right away, which
suggests a trend component).
e. Calculate the difference of the batting
averages from one year to the next.
Plot the difference series and also
compute its ACF. Does the plot show
that the variance of the original series
is reasonably stable? That is, are the
changes roughly the same size at the
beginning, middle, and end of the
series?
f. Looking at the ACF of the differenced
series, do you see much correlation
after the fi rst few lags? If not, it sug-
gests that the differenced series does
not have a trend, and this is what you
would expect. Interpret any lags that
are signifi cantly correlated.
g. Perform one-parameter exponential
smoothing forecasting one year ahead,
using w values of 0.2, 0.3, 0.4, and
0.5. In each case, notice the value
predicted for 2003 (observation 103).
Which parameter gives the lowest
standard error?
h. Save your changes to the workbook
and write a report summarizing your
observations.
- The Electric workbook has monthly data
on U.S. electric power production, 1978
through 1990. The variable called power
is measured in billions of kilowatt
hours. The fi gures come from the 1992
CRB Commodity Year Book, published
by the Commodity Research Bureau in
New York.
a. Open the Electric workbook from
the Chapter11 folder and save it as
Electric Analysis.
b. Create a line chart of the power data.
Is there any seasonality to the data?
c. Fit a three-parameter exponential
model with location, linear, and sea-
sonal parameters. Use a smoothing
constant of 0.05 for the location
parameter, 0.15 for the linear parameter,
and 0.05 for the seasonal parameter.
What level of power production do
you forecast over the next 12 months?
d. Using the seasonal index, which are
the three months of highest power
production? Is this in accordance
with the plots you have seen? Does
it make sense to you as a consumer?
By what percentage does the busiest
month exceed the slowest month?
e. Repeat the exponential smoothing of
part b of Exercise 6 with the smooth-
ing constants shown in Table 11-7.
Table 11-7 Exponential Smoothing Constants
Location Linear Seasonal
0.05 0.30 0.05
0.15 0.15 0.05
0.15 0.30 0.05
0.30 0.15 0.05
0.30 0.30 0.05
f. Which forecasts give the smallest
standard error?
g. Save your changes to the workbook
and report your observations.
- The Visit workbook contains monthly
visitation data for two sites at the Kenai
Fjords National Park in Alaska from
January 1990 to June 1994. You’ll ana-
lyze the visitation data for the Exit
Glacier site.
a. Open the Visit workbook from the
Chapter11 data folder and save it as
Visit Analysis.
b. Create a line plot of visitation for Exit
Glacier versus year and month. Sum-
marize the pattern of visitation at Exit
Glacier between 1990 and mid-1994.
