2020/03/05 by Matthieu Garcin, Garcin, Matthieu · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistics Theory (math.ST) #Stock Market Forecasting Methods #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.2003.02566
openalex publication_date 2020/03/05 · arxiv created 2022/01/11 · arxiv updated 2022/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion X. But this method is biased when applied to a stationary version of X, in particular an inverse Lamperti transform of X, with a linear time contraction of parameter θ. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations and an application to a financial time series. While it appears that the maximum-likelihood method is more accurate than the adapted absolute-moment estimation, this last method is not uninteresting for two reasons: it makes it possible to confirm visually that the model is well specified and it is computationally more performing.