Olha Bodnar

CUSUM Control Schemes for Multivariate Time Series

Up to now only a few papers (e.g., Theodossiou (1993), Kramer and Schmid (1997)) dealt with the problem of detecting shifts in the mean vector of a multivariate time series. Here we generalize several well-known CUSUM charts for independent multivariate normal variables (Crosier (1988), Pignatiello and Runger (1990), Ngai and Zhang (2001)) to stationary Gaussian processes. We consider both modified control charts and residual charts.

SEQUENTIAL SURVEILLANCE OF THE TANGENCY PORTFOLIO WEIGHTS

In this paper we derive sequential procedures for monitoring the structure of the tangency portfolio. A new measure of the distance between the estimated weights and the weights of the holding portfolio is suggested which is used in the derivation of the control schemes. The results are applied in a situation that is practically relevant.

Sequential Procedures for Monitoring Covariances of Asset Returns

Time variability of the expected returns as well as the volatility of asset returns can be caused by changes in the fundamental factors; for example, changes in commodity prices, macroeconomic policy, market trading activity, technological development, governmental policies, and so on. This leads to the deviation of a selected optimal portfolio from the Markowitz efficient frontier that consists of all portfolios with the highest expected return for the given level of risk or with the smallest risk for a preselected profit and, thus, is fully defined by the first two moments of asset returns (Markowitz, 1952). Changes in these characteristics are subject to structural breaks of the efficient frontier location in the mean-variance space and the optimal portfolios allocated on it.

On The Unbiased Estimator Of The Efficient Frontier

In the paper, we derive an unbiased estimator of the efficient frontier. It is shown that the suggested estimator corrects the overoptimism of the sample efficient frontier documented in Siegel and Woodgate (2007). Moreover, an exact F-test on the efficient frontier is presented.

Surveillance of the covariance matrix based on the properties of the singular Wishart distribution

A methodology which allows applying the standard monitoring techniques for the mean behaviour of Gaussian processes in the detection of shifts in the covariance matrix is developed. Moreover, the proposed methodology allows the use of an estimator of the covariance matrix based on a single observation. An extensive simulation study reveals the advantages of the considered approach.

Estimation and inference for dependence in multivariate data

In this paper, a new measure of dependence is proposed. Our approach is based on transforming univariate data to the space where the marginal distributions are normally distributed and then, using the inverse transformation to obtain the distribution function in the original space. The pseudo-maximum likelihood method and the two-stage maximum likelihood approach are used to estimate the unknown parameters. It is shown that the estimated parameters are asymptotical normally distributed in both cases. Inference procedures for testing the independence are also studied.

Discussion on “Optimal Sequential Surveillance for Finance, Public Health, and Other Areas” by Marianne Frisén

Abstract In the stimulating article by Marianne Frisén, a general overview about sequential surveillance is presented. Many applications of sequential surveillance in various fields of science are given. Although sequential surveillance has been successfully applied in engineering for more than 70 years, the extension to areas such as finance and medicine is not straightforward because completely new problems arise in practice. In our discussion of the article, we want to focus on this aspect and we will describe some of these points.

Application of the Generalized Likelihood Ratio Test for Detecting Changes in the Mean of Multivariate GARCH Processes

We derive several multivariate control charts to monitor the mean vector of multi-variate GARCH processes under the presence of changes, by means of maximizing the generalized likelihood ratio. This presentation is rounded up by a comparative performance study based on extensive Monte Carlo simulations. An empirical illustration shows how the obtained results can be applied to real data.