Stable law estimation functions

A collection of methods to estimate the four parameters of stable laws. The package also provides functions to compute the characteristic function and tools to run Monte Carlo simulations.

Details

The main functions of the package are briefly described below:

main function:

Estim is the most useful function of the package. It estimates of the parameters and the asymptotic properties of the estimators.

estimation function:

the methods provided so far are the maximum-likelihood (MLParametersEstim), the generalised method of moment with finite (GMMParametersEstim) or continuum (CgmmParametersEstim) moment conditions, the iterative Koutrouvelis regression method (KoutParametersEstim) and the fast Kogon-McCulloch method used for first guess estimation (IGParametersEstim).

characteristic function:

the characteristic function (ComplexCF) and its Jacobian (jacobianComplexCF) can be computed and will return a vector (respectively a matrix) of complex numbers.

Monte Carlo simulation

Estim_Simulation is a tool to run Monte Carlo simulations with flexible options to select the estimation method, the Monte Carlo control parameters, compute statistical summaries or save results to a file.

Author

Tarak Kharrat, Georgi N. Boshnakov

Note

Version 1 of this package had a somewhat restricted license since it needed package akima in some computations.

In version 2 of the package we implemented a 2D interpolation routine and removed the dependency on akima. Therefore, StableEstim is now under GPL license. The package is related to upcoming work by the authors where the different methods are compared using MC simulations.

See also

fBasics:::.mleStableFit, fBasics:::.qStableFit

package stabledist

References

Carrasco M and Florens J (2000). “Generalization of GMM to a continuum of moment conditions.” Econometric Theory, 16(06), pp. 797–834.

Carrasco M and Florens J (2002). “Efficient GMM estimation using the empirical characteristic function.” IDEI Working Paper, 140.

Carrasco M and Florens J (2003). “On the asymptotic efficiency of GMM.” IDEI Working Paper, 173.

Carrasco M, Chernov M, Florens J and Ghysels E (2007). “Efficient estimation of general dynamic models with a continuum of moment conditions.” Journal of Econometrics, 140(2), pp. 529–573.

Carrasco M, Florens J and Renault E (2007). “Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization.” Handbook of econometrics, 6, pp. 5633–5751.

Carrasco M and Kotchoni R (2010). “Efficient estimation using the characteristic function.” Mimeo. University of Montreal.

Nolan J (2001). “Maximum likelihood estimation and diagnostics for stable distributions.” L'evy processes: theory and applications, pp. 379–400.

nolan:2012StableEstim

Hansen LP (1982). “Large sample properties of generalized method of moments estimators.” Econometrica: Journal of the Econometric Society, pp. 1029–1054.

Hansen LP, Heaton J and Yaron A (1996). “Finite-sample properties of some alternative GMM estimators.” Journal of Business & Economic Statistics, 14(3), pp. 262–280.

Feuerverger A and McDunnough P (1981). “On efficient inference in symmetric stable laws and processes.” Statistics and Related Topics, 99, pp. 109–112.

Feuerverger A and McDunnough P (1981). “On some Fourier methods for inference.” Journal of the American Statistical Association, 76(374), pp. 379–387.

Schmidt P (1982). “An improved version of the Quandt-Ramsey MGF estimator for mixtures of normal distributions and switching regressions.” Econometrica: Journal of the Econometric Society, pp. 501–516.

Besbeas P and Morgan B (2008). “Improved estimation of the stable laws.” Statistics and Computing, 18(2), pp. 219–231.