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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 )