Serial Dependence and Rescaled Range Analysis

This paper discusses serial dependence from both a theoretical and an empirical perspective. Rescale Range Analysis (RRA), Hurst exponents, Autoregressive Integrated Moving Average (ARIMA) models and Fractal Brownian Motions (FBM) are some of the concepts discussed and analyzed. Daily and monthly SP-500 data from 2003 to 2009 are investigated. We find that returns tend to be serially independent, whereas volatility and expected returns tend to be positively serially correlated. This has not been clearly understood previously