In this article, we concentrate on various techniques to quantify long-range dependence: wavelets, Geweke and Porter-Hudak (GPH)'s semi-parametric method, the periodogram method, rescaled range analysis (R/S) and a modification of it aimed at accommodating for short memory, quasi maximum likelihood (QML), de-trended fluctuation analysis (DFA), Modified DFA (MDFA), and Centered Moving Average (CMA) analysis. Based on Monte Carlo experiments, we conclude that if the data generating process (DGP) is an AR(1), MA(1) or ARMA(1, 1) process, with moderate parameter values, the periodogram, GPH, QML, and modified R/S methods, followed by the DFA, MDFA, and CMA ones, perform reasonably well as regards with bias, although some of these techniques exhibit a non-negligible size distortion. Moreover, the QML, the periodogram, DFA, MDFA, and CMA methods overall provide with powerful and low-bias estimators, under alternative ARFIMA (p, d, q)-DGPs. The wavelet-based estimator in turn has high power, but it is noticeably upward (downward) biased when the autoregressive (moving-average) coefficient of the DGP is large. Our Monte Carlo experiments are complemented with an application to Dow Jones AIG Gold Sub-index data, by means of bootstrap re-sampling.
- quasi maximum likelihood