Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application

Abstract

Since the seminal paper of Granger & Joyeux (1980), the concept of a long memory has focused the attention of many statisticians and econometricians trying to model and measure the persistence of stationary processes. Many methods for estimating d, the long-range dependence parameter, have been suggested since the work of Hurst (1951). They can be summarized in three classes: the heuristic methods, the semi-parametric methods and the maximum likelihood methods. In this paper, we try by simulation, to verify the two main properties of d-super-ˆ: the consistency and the asymptotic normality. Hence, it is very important for practitioners to compare the performance of the various classes of estimators. The results indicate that only the semi-parametric and the maximum likelihood methods can give good estimators. They also suggest that the AR component of the ARFIMA (1, d, 0) process has an important impact on the properties of the different estimators and that the Whittle method is the best one, since it has the small mean squared error. We finally carry out an empirical application using the monthly seasonally adjusted US Inflation series, in order to illustrate the usefulness of the different estimation methods in the context of using real data.Long memory, ARFIMA ( p d q ) process, fractional Gaussian noise, Monte Carlo study,

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

“…where C 1 is a constant and is satisfied by some α ∈ (0, 1) (Boutahar et al, 2007;Beran et al, 2013). Equivalently, X t is a long-memory process if, in the spectral domain, the condition…”

“…The fractional differencing parameter d is related to the parameter α in Eq. (2) as follows: (Beran et al, 2013;Witt and Malamud, 2013). In addition to a slowly decaying ACF, a long-memory process manifests itself in two other equivalent fashions.…”

“…Here we provide a review of the definitions of such processes and several typical modeling approaches, including both time-domain and frequency-domain techniques, with special attention to their reconciliation. For a more comprehensive review, readers are referred to Beran et al (2013), Boutahar et al (2007), and Witt and Malamud (2013). Strictly speaking, X t is called a stationary long-memory process if the condition…”

“…where ω is angular frequency (Boutahar et al, 2007). One popular model for describing long-memory processes is the so-called fractional autoregressive integrated movingaverage model, or ARFIMA (p, q, d), which is an extension of ARMA models and is defined as follows:…”

On a class of estimation and test for long memory

“…Corresponding work include Geweke and Porter-Hudak (1983), Haslett and Raftery (1989), Beran (1994), Robinson (1995Robinson ( , 2005, among many others. Lo (1991), Baillie (1996), Giraitis et al (2003), Robinson (2003), Palma (2007) and Boutahar et al (2007) provided relevant literature review in detail.…”