Maximum likelihood estimation and diagnostics for stable distributions

By John P. Nolan. 2001

313 citations recorded by the source corpus.

A program for maximum likelihood estimation of general stable parameters is described. The Fisher information matrix is computed, making large sample estimation of stable parameters a practical tool. In addition, diagnostics are developed for assessing the stability of a data set. Applications to simulated data, stock price data, foreign exchange rate data, radar data, and ocean wave energy are presented.

Subfields: Atmospheric Science, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/2aaa828a6d20e7eefb1a8c0e257c3157551876d7

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Citations in the corpus

Machine Learning of Space-Fractional Differential Equations (2018, methodology): “Much more reliable methods include maximum likelihood estimation [20] and the generalized method of moments [7], which have had good success in practice.”
Goodness-of-fit tests for symmetric stable distributions—Empirical characteristic function approach (2006, methodology): “Although explicit forms of the density and the derivatives are not available for stable distributions, the method suggested by Matsui and Takemura (2006) which improves the original method of Nolan (1977,2001) gives very accurate approximations.”
SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling (2003, methodology): “Recently, Nolan showed that ML estimation of stable parameters is feasible by designing an efficient program [27].”
The Method of Simulated Quantiles (2013, unknown): “Since it is a complicated integral, even difficult to evaluate numerically, estimation by ML has been often not considered in applied work (though the theoretical properties of the ML estimator exist, Dumouchel, 1973, and the actual estimation has been performed by Nolan, 2001).”
Volatility estimators for discretely sampled Lévy processes (2007, background): “equation (see, e.g., [8, 10, 18, 19] and Chapter 4 in [23]), maximum likelihood by Fourier inversion of the characteristic function (see [9]), a regression based on the explicit form of the characteristic function (see [14]) or other numerical approximations (see [16, 17 ]).”
Coupled continuous time random walks in finance (2006, methodology): “08 (not shown), where the parameters were found via the maximum likelihood procedure of Nolan [17].”
Novel Bayesian multiscale method for speckle removal in medical ultrasound images (2001, methodology): “In particular, Zonget al.apply soft thresholding at fine scales (levels 1 and/or 2) and hard thresholding within middle levels 3 and/or 4 to eliminate noise, followed by nonlinear processing of feature energy to enhance contrast.”
Models for Heavy-tailed Asset Returns (2010, methodology): “Mittnik et al. (1999) utilized the FFT approach for approximating the stable density function, whereas Nolan (2001) used the direct integration method.”
Some Improvements in Numerical Evaluation of Symmetric Stable Density and Its Derivatives (2004, methodology): “Nolan (1997) gave accurate algorithms for general stable densities based on integral representations of the densities which were derived by Zolotarev (1986).”
Multivariate elliptically contoured stable distributions: theory and estimation (2013, methodology): “And there are fast methods to simulate stable r.v.s and several methods of estimating stable parameters based on maximum likelihood, quantiles, empirical characteristic functions, and fractional moments, see Nolan (2001).”
A simple approach to maximum intractable likelihood estimation (2013, methodology): “Various numerical approximations of the MLE have been proposed (see e.g. Nolan, 2001).”
Modeling financial data with stable distributions (2003, methodology): “It uses the Deutsch Mark exchange rate data (log ratios of successive values) described above.”
Diverging Moments and Parameter Estimation (2005, background): “Defining when exactly this asymptotic behavior starts seems to be a tough problem (see Nolan 2001), because it depends heavily on the parameterization used to model the distribution (in the parametric context).”
Maximum likelihood estimation for α-stable autoregressive processes (2009, methodology): “(Values for I −1(·) not given in Nolan [31] can be computed using the STABLE library.)”