Download erratum

100
JOURNAL OF MARKETING RESEARCH, FEBRUARY 1981
the 95% probability limits of the forecasts.
Clearly time series analysis is widely applicable in
marketing research. An important advantage is the
ability to predict and explain both short- and long-term
effects. However, the care must be taken in modeling
economic time series as the simple strategies of differencing data by prevailing techniques may not yield
reliable forecasts. Our time series modeling procedure
is different from the Box-Jenkins method in two main
aspects. First, it avoids the tedious stage of identifying
orders n and m of the ARMA(«,m) model from the
examination of plots of the estimated autocorrelation
and partial autocorrelation functions as recommended
in Box-Jenkins procedure and provides a step-by-step
modeling strategy which can be easily executed on
a digital computer to obtain the statistically adequate
model irrespective of its order.
The second difference is in the modeling of nonstationary time series. Box and Jenkins use the word
"nonstationary" for discrete ARMA models with one
or more roots with absolute value one, e.g. random
walk, EWMA, etc. However, the probabilistic properties are still independent of the origin, although theoretically their variance is infmite. As a matter of fact
in nonstationary cases, where trends and seasonality
are dominant in the data, the sample autocorrelation
functions fail to damp out quickly. Thus, tentative
identification of the model from their plots is almost
impossible. That is the reason for applying differencing
or seasonality operators (which in turn must be guessed
from the data or sample autocorrelation functions,
etc.). The danger of such an indiscriminate operating
or smoothing of the data merely to simplify analysis
has been pointed by Slutsky [1927]. Such an operation
itself may introduce spurious trends and periods in
the resultant series which are not present in the data.
The final fitted model, though statistically adequate
and apparently parsimonious, may give a completely
distorted picture ofthe structure ofthe original series.
Our use of the term "nonstationary" when the
nature of a series of data appears to be dependent
on time origin follows the terminology in stochastic
processes, systems analysis, and control theory. The
models for such a series of data therefore need to
include functions which depend on time origin.
REFERENCES
Box, G. E. P. andG. M. Jenkins (1970), Time Series Analysis,
Forecasting, and Control. San Francisco: Holden-Day.
Brown, R. G. (1962), Smoothing, Forecasting, and Prediction
of Finite Time Series. Englewood Cliffs, New Jersey:
Prentice Hall, Inc.
Geurts, M. D. and L B. Ibrahim (1975), "Comparing the
Box-Jenkins Approach with the Exponentially Smoothed
Forecasting Model with an Application to Hawaii
Tourists," Journal of Marketing Research, 12 (May),
182-7.
Helmer, R. M. and J. K. Johansson (1977), "An Exposition
of the Box-Jenkins Transfer Function Analysis with an
Application to the Advertising-Sales Relationship," Journal of Marketing Research, 14 (May), 227-39.
Mabert, V. A. and R. C. Radcliffe (1974), "A Forecasting
Methodology as Applied to Financial Time Series," Accounting Review (January), 61-75.
Moriarty, M. and A. Adams (1979), "Issues in Sales Territory
Modeling and Forecasing Using Box-Jenkins Analysis,"
Journal of Marketing Research, 16 (May), 221-32.
Pindyck, R. S. and D. L. Rubenfeld (1976), Econometric
Models and Economic Forecasts. New York, McGrawHill Book Company.
Slutsky, E. (1927), "The Summation of Random Causes
as the Source of Cyclic Processes" (Russian with English
summary). Problems of Economic Conditions (Institute
of Economic Conjecture, Moscow), 3, revised English
ed. in Econometrika, 5, 105 (1937).
Tiao, G. C. and D. J. Pack (1975), "Modeling the Consumption of Frozen Concentrated Orange Juice: A Case Study
of Time Series Analysis," Academic Economic Papers,
3 (February).
Wu, S. M. (1977), "Dynamic Data System—A New Modeling Approach," ASME Transactions, SeriesB, 99, 708-14.
ERRATUM
The article "Measuring Personal Values: An Evaluation of Alternative Methods" by Thomas J. Reynolds
and James P. Jolly in the November 1980 JMR contains an error in the formula for transforming 'raUfi. The
correct formula is:
concordant pairs
V Vtotal - 1/22/,(/, - 1) V t o t a l - l / 2 2 / , ( / , - • 1 )