Analytical Formulation of Bubble Entropy for Autoregressive Processes

Bubble Entropy is a recently proposed entropy metric, that is almost free of parameters. Up to date, only an operational formulation of Bubble Entropy was available. In this paper, we derived analytical formulations of Bubble Entropy for embedding dimensions m ≤ 3, when the time series is generated by a stationary Gaussian autoregressive process. Such formulations match with the estimates obtained using Monte Carlo simulations. The study allows to further investigate the mathematical properties of Bubble Entropy on stationary autoregressive processes.