Sample Size Recommendations for Continuous-Time Models: Compensating Shorter Time Series with Larger Numbers of Persons and Vice Versa

Abstract

Autoregressive modeling has traditionally been concerned with time-series data from one unit (N = 1). For short time series (T < 50), estimation performance problems are well studied and documented. Fortunately, in psychological and social science research, besides T, another source of information is often available for model estimation, that is, the persons (N > 1). In this work, we illustrate the N/T compensation effect: With an increasing number of persons N at constant T, the model estimation performance increases, and vice versa, with an increasing number of time points T at constant N, the performance increases as well. Based on these observations, we develop sample size recommendations in the form of easily accessible N/T heatmaps for two popular autoregressive continuous-time models.