Univariate measures of persistence: A comparative analysis

Persistence is the speed with which a time series returns to its mean after a shock. Although several measures of persistence have been proposed in the literature, when they are empirically applied, the different measures indicate incompatible messages, as they differ both in the level and the implied evolution of persistence. One plausible reason why persistence estimators may differ is the presence of data particularities such as trends, cycles, measurement errors, additive and temporary change outliers, and structural changes. To gauge the usefulness and robustness of different measures of persistence, we compare them in a univariate time series framework using Monte Carlo simulations. We consider nonparametric, semiparametric, and parametric time-domain and frequency-domain persistence estimators and investigate their performance under different anomalies found in practice. Our results indicate that the nonparametric method is, on average, less affected by the different types of time series anomalies analyzed in this work.