Memory indicators and their incorporation into dynamic models
Data collected over time may exhibit some type of memory structure, such as a short or long term memory. Two commonly used indicators of memory are the Hurst exponent and the self-similarity index. We investigate the relationship between the Hurst exponent and the self-similarity index and show that the Hurst exponent is an estimator of the self-similarity index in some time series such as fractional Brownian motion. For time series with constant self-similarity index, we compare the statistical properties of various estimators of the self-similarity index via simulation for a range of nominal H-values between 0 and 1. We also employ windowing techniques to study the over-time behavior of the memory structure in a subset of the S&P500 series.