Indirect inference for stochastic volatility models via the log-squared observations.

Model; Models; Stochastic volatility; Volatility;

Indirect Inference for Stochastic Volatility Models via the Log-Squared Observations

An indirect estimator of the stochastic volatility (SV) model with AR(1) logvolatility is proposed. The estimator is derived as an application of the method of indirect inference (Gouriéroux, Monfort and Renault (1993)), using an auxiliary SV model that mimics the SV model of interest (which has latent volatility) but is constructed so as to make volatility observable. The resulting estimator works by fitting an AR(1) to the log-squared observations and then applying a simple transformation to the parameter estimates. A closed-form expression for the asymptotic covariance matrix of the estimator is also derived. The estimator is applied to the Brussels All Shares Price Index from January 1, 1980, to January 16, 2003.

Fully parameterized macromodeling of S-parameter data by interpolation of numerator & denominator

A robust approach for parametric macromodeling of tabulated frequency responses is presented. An existing technique is modified in such a way that interpolation is performed at the numerator and denominator level, rather than the transfer function level. This enhancement ensures that the poles of the parametric macromodel are fully parameterized. It strengthens the modeling capabilities and improves the model compactness

Symbolic macromodeling of parameterized S-parameter frequency responses

This paper presents an evolutionary algorithm for symbolic macromodeling of parameterized frequency responses. The method does not require an a priori specification of the multivariate functional form or complexity of the model. Numerical results are shown to illustrate the performance of the technique

Dimensionality reduction of optimization problems using variance based sensitivity analysis

We propose a new interaction index derived from the computation of Sobol indices. In optimization, interaction index can be used to detect lack of interaction among input parameters. First order interaction indices if they return zero, means that those parameters can be optimized independently holding other parameters constant. Likewise, second order interaction indices can tell if a combination of two parameter can be optimized independently of other parameters. In this way, the original optimization problem may be decomposed into a set of lower dimensional problems which may then be solved independently and in parallel. The interaction indices can potentially be useful in robust optimization as well, since it provides importance measure in minimizing output variances

Adaptive initial step size selection for simultaneous perturbation stochastic approximation

A difficulty in using Simultaneous Perturbation Stochastics Approximation (SPSA) is its performance sensitivity to the step sizes chosen at the initial stage of the iteration. If the step size is too large, the solution estimate may fail to converge. The proposed adaptive stepping method automatically reduces the initial step size of the SPSA so that reduction of the objective function value occurs more reliably. Ten mathematical functions each with three different noise levels were used to empirically show the effectiveness of the proposed idea. A parameter estimation example of a nonlinear dynamical system is also included

Asymptotic properties of GMM estimators of stochastic volatility.

Estimator; Stochastic volatility; Volatility;