Robust PCA for high-dimensional data based on characteristic transformation

In this paper, we propose a novel robust principal component analysis (PCA) for high-dimensional data in the presence of various heterogeneities, in particular strong tailing and outliers. A transformation motivated by the characteristic function is constructed to improve the robustness of the classical PCA. The suggested method has the distinct advantage of dealing with heavy-tail-distributed data, whose covariances may be non-existent (positively infinite, for instance), in addition to the usual outliers. The proposed approach is also a case of kernel principal component analysis (KPCA) and employs the robust and non-linear properties via a bounded and non-linear kernel function. The merits of the new method are illustrated by some statistical properties, including the upper bound of the excess error and the behaviour of the large eigenvalues under a spiked covariance model. Additionally, using a variety of simulations, we demonstrate the benefits of our approach over the classical PCA. Finally, using data on protein expression in mice of various genotypes in a biological study, we apply the novel robust PCA to categorise the mice and find that our approach is more effective at identifying abnormal mice than the classical PCA.     

Portfolio value-at-risk estimation for spot chartering decisions under changing trade patterns: A copula approach

Evolving geopolitical relationships between countries (especially between China and the United States) in recent years have highlighted dynamically changing trade patterns across the globe, all of which elevate risk and uncertainty for transport service providers. In order to mitigate risks, shipowners and operators must be able to estimate risks appropriately; one potentially promising method of doing so is through the value-at-risk (VaR) method. VaR describes the worst loss a portfolio is likely to sustain, which will not be exceeded over a target time horizon at a given level of confidence. This article proposes a copula-based GARCH model to estimate the joint multivariate distribution, which is a key component in VaR estimation. We show that the copula model can capture the VaR more successfully, as compared with the traditional method of calculation. As an empirical study, the expected portfolio VaR is examined when a shipowner chooses among Panamax soybean trading routes under a condition of reduced trade volumes between the United States and China due to the ongoing trade turmoil. This study serves as one of the very few papers in the literature on shipping portfolio VaR analysis. The results have significant implications for shipowners regarding fleet repositioning, decision making, and risk management.