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The property of long memory and its parameter estimate are important in financial econometrics. This paper proposes a novel Bayesian approach to estimate the fractional differencing order and compares its performance with rescaled range analysis (R/S), detrended fluctuation analysis (DFA) and detrended moving average (DMA), based on the fractal Brownian motion sequence simulated by the ARFIMA model. The results indicate that the estimation accuracy of the Bayesian approach is significantly improved and is less volatile than R/S and DFA methods. We adopt mean absolute error and standard deviation as the criteria for measuring the finite sample performance of the estimators. To check robust results, four different methods (i.e. the Gelman–Rubin diagnostic, the Geweke diagnostic, the Heidelberger–Welch diagnostic, the Raftery–Lewis diagnostic) are simultaneously implemented to monitor the convergence of the posterior distribution in the Bayesian methodology. Therefore, the long memory estimator from the Bayesian model is preferred according to the results in this paper.

A novel Bayesian approach to estimate long memory parameter