Temporal Aggregation, the Data Interval Bias, and Empirical Estimation of Bimonthly Relations from Annual Data
解释了为何使用年度数据会高估广告对销售影响的持续时间，并展示了如何从年度数据中恢复双月参数，对研究广告效果的学者有用。
In an important study reviewing the literature on econometric studies of the relationship between advertising and sales Clarke (Clarke, Darral G. 1976. Econometric measurement of the duration of advertising effects on sales. J. Marketing Res. 13 (November) 345–357.) concluded that the implied duration interval of the effects of advertising on sales were too long when the studies used annual data. A theoretical explanation is provided here for the observation of parameter estimates which vary with the data interval employed in the analysis. Parameter estimates are developed on the basis of data aggregated at various levels of temporal aggregation and compared with theoretical values. It is demonstrated that it is possible to recover bimonthly parameters when only annual data are available.