A Method for Asynchronous Time Series Analysis with Marketing Applications
提出一种无需数据预处理的异步时间序列状态空间模型估计方法，通过模拟和营销应用（广告测试、营销组合模型）证明其能避免数据聚合导致的参数偏差，适用于不同频率的营销指标分析。
Many time series data evolve asynchronously. In marketing, for example, we observe ad liking every second, hourly clickstreams, daily sales, weekly brand awareness, or monthly ad expenditures. Thus, the question arises: how to estimate dynamic models when metrics evolve at different frequencies? To this end, we develop a new method for estimation and inference of state space models for asynchronous data. In contrast to existing approaches, the proposed method does not require any data preprocessing to align frequencies. We derive the optimal gain factor from first principles and demonstrate in three simulation studies that the new method recovers model parameters as accurately as the full-information Kalman filter as if all data were available. This finding holds across various degrees of noise levels and data sparsity. More importantly, we show that ignoring data asynchronicity results in substantially biased parameter estimates. Empirically, we illustrate the efficacy of the new method via two applications: copy testing of an advertisement and a marketing mix model, both with asynchronous data. It yields meaningful results compared with those obtained by aligning asynchronous data to the slowest frequency (i.e., data aggregation). In the marketing mix application, for example, data aggregation produces erroneously insignificant estimates of sales carryover and TV effectiveness, and these become significant when we apply the new method. These biased estimates can have serious managerial consequences. Thus, the proposed method paves the way to analyze asynchronous time series data: slow- or fast-moving dependent variables, slow- or fast-moving independent variables, and all of them at equal or unequal frequencies. This paper was accepted by Eric Anderson, marketing. Funding: This work was supported by the Marketing Science Institute [Grant 4-1959]. P. A. Naik acknowledges the financial support received from the University of California Davis travel and small research grants program across 2015–2024. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.04336 .