No abstract

Barndorff-Nielsen and Shephard (2001) proposed a class of stochastic volatility models in which the volatility follows the Ornstein-Uhlenbeck process driven by a positive Levy process without the Gaussian component. The parameter estimation of these models is challenging because the likelihood function is not available in a closed-form expression. A large number of estimation techniques have been proposed, mainly based on Bayesian inference. The main aim of the paper is to present an application of iterated filtering for parameter estimation of such models. Iterated filtering is a method for maximum likelihood inference based on a series of filtering operations, which provide a sequence of parameter estimates that converges to the maximum likelihood estimate. An application to S&P500 index data shows the model perform well and diagnostic plots for iterated filtering ensure convergence iterated filtering to maximum likelihood estimates. Empirical application is accompanied by a simulation study that confirms the validity of the approach in the case of Barndorff-Nielsen and Shephard's stochastic volatility models.

In financial applications, understanding the asset correlation structure is crucial to tasks such as asset pricing, portfolio optimisation, risk management, and asset allocation. Thus, modelling the volatilities and correlations of multivariate stock market returns is of great importance. This paper proposes the iterated filtering algorithm for estimating the bivariate stochastic volatility model of Yu and Meyer. The iterated filtering method is a frequentist-based approach that utilises particle filters and can be applied to estimating the parameters of non-linear or non-Gaussian state-space models. The paper presents an empirical example that demonstrates the way in which the proposed estimation method might be used to estimate the correlation between the returns of two assets: Standard and Poor’s 500 index and the price of gold in US dollars. This is accompanied by a simulation study that proves the validity of the approach.

Univariate normality tests are typically classified into tests based on empirical distribution, moments, regression and correlation, and other. In this paper, power comparisons of nine normality tests based on measures of moments via the Monte Carlo simulations is extensively examined. The effects on power of the sample size, significance level, and on a number of alternative distributions are investigated. None of the considered tests proved uniformly most powerful for all types of alternative distributions. However, the most powerful tests for different shape departures from normality (symmetric short-tailed, symmetric long-tailed or asymmetric) are indicated.

The beta parameter is a popular tool for the evaluation of portfolio performance. The Sharpe single-index model is a simple regression model in which the stock's returns are regressed against the returns of a broader index. The beta parameter is a measure of the strength of this relation. Extensive recent research has proved that the beta is not constant in time and should be modelled as a time-variant coefficient. One of the most popular methods of the estimation of a time-varying beta is the Kalman filter. As the output of the Kalman filter, one obtains a sequence of the estimates of a time-varying beta. This sequence shows the historical dynamics of sensitivity of a company's returns to the variations of market returns. The article proposes a method of clustering companies listed on the Warsaw Stock Exchange according to time-varying betas.