Sample Size Recommendations for Continuous-Time Models: Compensating Shorter Time Series with Larger Numbers of Persons and Vice Versa
Martin Hecht, Steffen Zitzmann
Abstract
Autoregressive modeling has traditionally been concerned with time-series data from one unit (<i>N</i> = 1). For short time series (<i>T</i> T, another source of information is often available for model estimation, that is, the persons (<i>N</i> > 1). In this work, we illustrate the <i>N</i>/<i>T</i> compensation effect: With an increasing number of persons <i>N</i> at constant <i>T</i>, the model estimation performance increases, and vice versa, with an increasing number of time points <i>T</i> at constant <i>N</i>, the performance increases as well. Based on these observations, we develop sample size recommendations in the form of easily accessible <i>N</i>/<i>T</i> heatmaps for two popular autoregressive continuous-time models.