Oliver Grothe

Tracking Changes in Cardiac Output: Statistical Considerations on the 4-quadrant Plot and the Polar Plot Methodology

When comparing 2 technologies for measuring hemodynamic parameters with regard to their ability to track changes, 2 graphical tools are omnipresent in the literature: the 4-quadrant plot and the polar plot recently proposed by Critchley et al. The polar plot is thought to be the more advanced statistical tool, but care should be taken when it comes to its interpretation. The polar plot excludes possibly important measurements from the data. The polar plot transforms the data nonlinearily, which may prevent it from being seen clearly. In this article, we compare the 4-quadrant and the polar plot in detail and thoroughly describe advantages and limitations of each. We also discuss pitfalls concerning the methods to prepare the researcher for the sound use of both methods. Finally, we briefly revisit the Bland-Altman plot for the use in this context.

Novelty filtering with a photorefractive lithium–niobate crystal

In this letter we present a technique which employs a photorefractive lithium–niobate crystal for novelty filtering. Due to the minimal trail formation exhibited by this novelty filter, it can be used for reliable quantitative phase measurement for time intervals of the order of a few hours. We present a simplified theoretical description of this filter based on a coupled wave theory [N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979); N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics22, 961 (1979)]. We also demonstrate the first experimental results of employing this device in the field of microfluid dynamics for measuring the concentration changes produced due to the mixing of two transparent liquids in a microchannel.

Estimating correlation and covariance matrices by weighting of market similarity

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for the similarity of previous market conditions to the present situation. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure that compares the current correlation structure of the market to the structures at past times. Similarity is then measured by the matrix 2-norm of the difference of probe correlation matrices estimated for two different points in time. The method is validated in a simulation study and tested empirically in the context of mean–variance portfolio optimization. In the latter case we find an enhanced realized portfolio return as well as a reduced portfolio risk compared with alternative approaches based on different strategies and estimators.

Vine Constructions of Levy Copulas

Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dimensions. To overcome this problem, the concept of pair-copula constructions has been successfully applied to distributional copulas. In this paper, we develop the pair Levy copula construction (PLCC). Similar to pair constructions of distributional copulas, the pair construction of a d-dimensional Levy copula consists of d(d−1)/2 bivariate dependence functions. We show that only d−1 of these bivariate functions are Levy copulas, whereas the remaining functions are distributional copulas. Since there are no restrictions concerning the choice of the copulas, the proposed pair construction adds the desired flexibility to Levy copula models. We discuss estimation and simulation in detail and apply the pair construction in a simulation study. To reduce the complexity of the notation, we restrict the presentation to Levy subordinators, i.e., increasing Levy processes.

Construction and sampling of Archimedean and nested Archimedean Lévy copulas

The class of Archimedean Levy copulas is considered with focus on the construction and sampling of the corresponding Levy processes. Furthermore, the class of nested Archimedean Levy copulas is introduced. This class allows one to model hierarchical dependences between Levy processes. It also overcomes the symmetry of Archimedean Levy copulas. Finally, a new sampling algorithm for multivariate Levy processes with dependence structure specified by either Archimedean or nested Archimedean Levy copulas is derived from a Marshall-Olkin-type algorithm. In contrast to the widely used conditional sampling method, this algorithm does not require (inverses of) conditional Levy copulas to be known. It also does not suffer from an asymmetric bias introduced by the conditional sampling method in the Levy framework.

Models for short-term forecasting of spike occurrences in Australian electricity markets: A comparative study

Understanding the dynamics of extreme observations, so called spikes, in real-time electricity prices has a crucial role in risk-management and trading. Yet the contemporaneous literature appears to be at the beginning of understanding the dierent mechanisms that drive spike probabilities. We reconsider the problem of short-term, i.e., half hourly, forecasts of spike occurrence in the Australian electricity market and develop models, tailored to capture the data properties. These models are variations of a dynamic binary response model, extended to allow for regime specic eects and an asymmetric link function. Furthermore, we study a recently proposed approach based on the autoregressive conditional hazard model. The proposed models use load forecasts and lagged log-prices as exogenous variables. Our in- and out-of-sample results suggest that some specications dominate and can therefore be recommended for the problem of spike forecasting.

Kendall's W reconsidered

In their seminal article, Kendall and Babington Smith (1939) suggested a measure 𝒲 to quantify the agreement between d rankings of n objects. Its distribution was essentially investigated under the assumption of independent rankings. In many applications, however, the rankings are not independent. This article reconsiders Kendalls 𝒲, investigating its distribution for dependent rankings using copula theory. We show that Kendalls 𝒲 is asymptotically normally distributed under very weak assumptions and that its variance can be estimated by means of bootstrap and jackknife. We present an application of Kendalls 𝒲 to returns and volatilities of the German DAX-30 assets.

A higher order correlation unscented Kalman filter

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential estimation of diffusion parameters, e.g., volatility, which are not correlated with the observations is not possible. While other filters overcome this problem with simulations, we extend the measurement update of the Gaussian two-moment filters by a higher order correlation measurement update. We explicitly state formulas for a higher order unscented Kalman filter within a continuous-discrete state space. We demonstrate the filter in the context of parameter estimation of an Ornstein-Uhlenbeck process.

Kendall's 𝒲 Reconsidered

In their seminal article, Kendall and Babington Smith (1939) suggested a measure 𝒲 to quantify the agreement between d rankings of n objects. Its distribution was essentially investigated under the assumption of independent rankings. In many applications, however, the rankings are not independent. This article reconsiders Kendalls 𝒲, investigating its distribution for dependent rankings using copula theory. We show that Kendalls 𝒲 is asymptotically normally distributed under very weak assumptions and that its variance can be estimated by means of bootstrap and jackknife. We present an application of Kendalls 𝒲 to returns and volatilities of the German DAX-30 assets.

On the length of copula level curves

Abstract Motivated by the well-known fact that the surface of copulas is closely related to common dependence measures such as Spearman’s rho, we investigate level curves of bivariate copulas and study their lengths. To this end, we establish the length profile L C ( t ) which maps each level t ∈ [ 0 , 1 ] to the length of the respective level curve. Some basic properties of the length profile, such as continuity and differentiability with respect to t , are examined. Based on the length profile, a measure l C is defined, which can be interpreted as the average level curve length. l C is a measure of association, it is, however, not a concordance measure in general. Some further, partially surprising properties, such as closed-form formulas of l C for completely dependent copulas, conclude the paper.