AR(p)-based detrended fluctuation analysis

Autoregressive models are commonly used for modeling time-series from nature, economics and finance. This work explored simple autoregressive AR(p) models to remove long-term trends in detrended fluctuation analysis (DFA). Crude oil prices and bitcoin exchange rate were considered, with the former corresponding to a mature market and the latter to an emergent market. Results showed that AR(p)-based DFA performs similar to traditional DFA. However, the former DFA provides information on stability of long-term trends, which is valuable for understanding and quantifying the dynamics of complex time series from financial systems.