Test to determine the Markov order of a time series

The Markov order of a time series is an important measure of the "memory" of a process, and its knowledge is fundamental for the correct simulation of the characteristics of the process. For this reason, several techniques have been proposed in the past for its estimation. However, most of this methods are rather complex, and often can be applied only in the case of Markov chains. Here we propose a simple and robust test to evaluate the Markov order of a time series. Only the first-order moment of the conditional probability density function characterizing the process is used to evaluate the memory of the process itself. This measure is called the "expected value Markov (EVM) order." We show that there is good agreement between the EVM order and the known Markov order of some synthetic time series.