482 Statistical Methods
It’s possible to set up similar spreadsheets for two-parameter and three-
parameter exponential smoothing, but that will not be demonstrated here.
The main diffi culty in setting up the spreadsheet to do these calculations is
in determining the initial estimates of S 0 , T 0 , and the seasonal indexes.
In the case of two-parameter exponential smoothing, you would use lin-
ear regression on the entire time series to derive initial estimates for the
location and trend values. Once this is done, you would derive the fore-
casted values using the recursive equations described earlier in the chap-
ter. You would then apply the Solver to minimize the mean square error
of the forecasts by modifying both the location and the trend smoothing
constants. Using the Solver to derive the best smoothing constants for the
three-parameter model is more complicated because you have to come
up with initial estimates for all of the seasonal indexes. The interested
student can refer to more advanced texts for techniques to calculate the
initial estimates.
You can now save and close the Exponential Smoothing workbook.Exercises
- Do the following calculations for one-
parameter exponential smoothing,
where w 50 .1 0 :
a. S 45 23.4 and y 5529. What is S 5?
b. If the observed value of y 6 is 25, what
is the value of S 6? Assume the same
values as in part a. - Do the following calculation for two-
parameter exponential smoothing,
where w 50 .1 0 and t 5 0.20:
a. S 45 23.4, T 45 1.1, and y 5529.
What is S 5? What is T 5?
b. If the observed value of y 6 is 25, what
are the values of S 6 and T 6? Assume
the same values as in part a. - If monthly sales are equal to 4,811 units
and the seasonal index for that month is
0.85, what is the adjusted sales fi gure? - How can you tell whether a series is
seasonal? Mention plots, including the
ACF. What is the difference between
additive and multiplicative seasonality?
5. A politician citing the latest raw monthly
unemployment fi gures claimed that
unemployment had fallen by 88,000
workers. The Bureau of Labor Statistics,
however, using seasonally adjusted
totals, claimed that unemployment had
increased by 98,000. Discuss the two in-
terpretations of the data. Which number
gives a better indication of the state of
the economy?
6. The Batting Average workbook contains
data on the leading major league
baseball batting averages for the years
1901 to 2002. Analyze these data.
a. Open the Batting Average workbook
from the Chapter11 folder and save it
as Batting Average Analysis.
b. Create a line chart of the batting aver-
age versus year. Do you see any appar-
ent trends? Do you see any outliers?
Does George Brett’s average of 0.390
in 1980 stand out compared with
other observations?