This paper puts forward a technique based on the characteristic function to tackle the problem of the sum of stochastic variables. We consider independent processes whose reduced variables are identically distributed, including those that violate the conditions for the central limit theorem to...

We consider a family of proper random variables which converges to an improper random variable. The limit in distribution is found and applied to obtain a closed-form expression for the limiting power of the Cliff-Ord test for autocorrelation. The applications include the theory of...

In this addendum to Carey (2005), we draw several more analogies with the Black-Scholes model. We derive the characteristic function of the underlying log process as a function of the volatilities of all orders. Option prices are shown to satisfy an infinite-order version of the Black-Scholes...

In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite location-scale mixtures and (ii) versions of approximate...

The paper aims to estimate the impact of calendar effects in volatility of the preferred and ordinary shares of Vale. The data researched were the stocks prices Vale between January 2, 1995 and October 26, 2011. The Stochastic Volatility Model was the Model and the Structural Model was the...

Maximum likelihood estimation of dynamic latent variable models requires to solve integrals that are not analytically tractable. Numerical approximations represent a possible solution to this problem. We propose to use the Adaptive Gaussian-Hermite (AGH) numerical quadrature approximation for a...