Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood
Restricted accessResearch articleFirst published online August, 1988
Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood
Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest that (1) IGLS and ML provide good estimates for the response parameters in instances of positive serial correlation, (2) ML provides superior (in mean squared error) estimates for the serial correlation coefficient, and (3) IGLS might have difficulty in deriving parameter estimates in instances of negative serial correlation.
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References
1.
BassFrank M., and ClarkeDarral G. (1972), “Testing Distributed Lag Models of Advertising Effect,”Journal of Marketing Research, 9(August), 298–308.
2.
BassFrank M., and LeoneRobert P. (1983), “Temporal Aggregation, the Data Interval Bias, and Empirical Estimation of Bimonthly Relations from Annual Data,”Management Science (January), 1–11.
3.
BassFrank M., and LeoneRobert P. (1986), “Estimating Micro Relationships from Macro Data: A Comparative Study of Two Approximations of the Brand Loyal Model Under Temporal Aggregation,”Journal of Marketing Reserach, 23(August), 291–7.
4.
BreuschTrevor S. (1980), “Useful Invariance Results for Generalized Regression Models,”Journal of Econometrics, 13(August), 327–40.
5.
ClarkeDarral G., and McCannJohn M. (1977), “Cumulative Advertising Effects: The Role of Serial Correlation; A Reply,”Decision Sciences, 8(April), 366–43.
6.
HoustonFranklin S., and WeissDoyle L. (1975), “Cumulative Advertising Effects: The Role of Serial Correlation,”Decision Sciences, 6(July), 471–81.
JudgeGregory G., and GriffithsW. E., and Carter HillR., and LutkepohlHelmut, and LeeTsoung-Chao (1985), The Theory and Practice of Econometrics.New York: John Wiley & Sons, Inc.
9.
KanetkarVinay, WeinbergCharles B., and WeissDoyle L. (1986a), “Recovering Micro Parameters from Aggregate Data for the Koyck and Brand Loyal Models,”Journal of Marketing Research,”, 23(August), 298–304.
10.
KanetkarVinay, WeinbergCharles B., and WeissDoyle L. (1986b), “Estimating Parameters of the Autocorrelated Current Effects Model from Temporally Aggregated Data,”Journal of Marketing Research, 23(November), 379–86.
11.
KendallM. G., and StuartA. (1973), The Advanced Theory of Statistics.New York: Hafner Press.
12.
KramerWalter (1980), “Finite Sample Efficiency of Ordinary Least Squares in the Linear Regression Model with Autocorrelated Errors,”Journal of the American Statistical Association, 75(December), 1005–09.
13.
OberhoferW., and KmentaJ. (1974), “A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models,”Econometrica, 42, 579–90.
14.
RaoPotluri, and GrilichesZvi (1969), “Small-Sample Properties of Several Two-Stage Regression Methods in Context of Autocorrelated Disturbances,”Journal of the American Statistical Association, 64(March), 253–72.
15.
TheilHenri (1971), Principles of Econometrics.New York: John Wiley & Sons, Inc.
16.
VanhonackerWilfried R. (1983), “Carryover Effects and Temporal Aggregation in a Partial Adjustment Model Framework,”Marketing Science, 2(Summer), 297–317.
17.
VanhonackerWilfried R. (1984), “Estimation and Testing of a Dynamic Sales Response Model with Data Aggregated Over Time: Some Results for the Autoregressive Current Effects Model,”Journal of Marketing Research, 21(November), 445–55.
18.
VanhonackerWilfried R. (1987), “Estimating the Duration of Dynamic Effects With Temporally Aggregated Observations,”Journal of Statistical Computation and Simulation, 27(April), 185–209.
19.
WeissDoyle L., HoustonFranklin S., and WindalPierre M. (1978), “The Periodic Pain of Lydia E. Pinkham,”Journal of Business, 51(January), 91–101.
20.
WeissDoyle L., WeinbergCharles B., and WindalPierre M. (1983), “The Effects of Serial Correlation and Data Aggregation on Advertising Measurement,”Journal of Marketing Research, 20(August), 268–79.
21.
WindalPierre M., and WeissDoyle L. (1980), “An Iterative GLS Procedure for Estimating the Parameters of Models with Autocorrelated Errors Using Data Aggregated Over Time,”Journal of Business, 53(October), 415–24.
