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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.

Measures of association are suggested between two random vectors. The measures are copula-based and therefore invariant with respect to the univariate marginal distributions. The measures are able to capture positive as well as negative association. In case the random vectors are just random variables, the measures reduce to Kendall's tau or Spearman's rho. Nonparametric estimators, based on ranks, for the measures are derived. Their large-sample asymptotics are derived and their small-sample behavior is investigated by simulation. The measures are applied to characterize strength and direction of association of northern and southern European bond markets during the recent Euro crisis as well as association of stock markets with bond markets.

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.

We study the prediction performance of different improved individual wind energy forecasts in various static and dynamic combination processes. To this end, we develop a combined error minimization model (CEMM) based on nonlinear functions. This approach reflects the nonlinear nature of weather and especially of wind energy prediction problems. Based on the model, we construct significantly improved individual forecasts. The corresponding time dependent model coefficients are determined by dynamic OLS (ordinary least squares) regression and Kalman filter methods. The former method shows a slightly better performance than the Kalman filter based approaches. Further improvements can be achieved by a combination of these improved wind energy forecasts. In this case, the combination coefficients are calculated from a static and two dynamic OLS regressions. The resulting forecasts are characterized by a further increased prediction accuracy compared to the combination of the uncorrected forecast data and can outperform a given benchmark.

This paper investigates the dependence of extreme jumps in multivariate Levy processes. We introduce a measure called jump tail dependence, defined as the probability of observing a large jump in one component of a process given a concurrent large jump in another component. We show that this measure is determined by the Levy copula alone and that it is independent of marginal Levy processes. We derive a consistent nonparametric estimator for jump tail dependence and establish its asymptotic distribution. Regarding the economic relevance of the measure, a simulation study illustrates that jump tail dependence has a substantial impact on financial portfolio distributions and optimal portfolio weights.

The investment decision on the placement of wind turbines is, neglecting legal formalities, mainly driven by the aim to maximize the expected annual energy production of single turbines. The result is a concentration of wind farms at locations with high average wind speed. While this strategy may be optimal for single investors maximizing their own return on investment, the resulting overall allocation of wind turbines may be unfavorable for energy suppliers and the economy because of large fluctuations in the overall wind power output. This paper investigates to what extent optimal allocation of wind farms in Germany can reduce these fluctuations. We analyze stochastic dependencies of wind speed for a large data set of German on- and offshore weather stations and find that these dependencies turn out to be highly nonlinear but constant over time. Using copula theory we determine the value at risk of energy production for given allocation sets of wind farms and derive optimal allocation plans. We find that the optimized allocation of wind farms may substantially stabilize the overall wind energy supply on daily as well as hourly frequency.

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 Kendall's 𝒲, investigating its distribution for dependent rankings using copula theory. We show that Kendall's 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 Kendall's 𝒲 to returns and volatilities of the German DAX-30 assets.

Student’s t -distributions are widely used in financial studies as heavy-tailed alternatives to normal distributions. As these distributions are not closed under convolution, there exist no Levy processes with Student’s t -marginals at all points in time. In this article we show that a Student’s t -approximation of these marginals is still suitable, while not exact. Using this approximation, we are able to describe the scaling behavior of such Levy–Student processes and the parameters of its marginal distributions by a simple analytical scaling law. This scaling law drastically simplifies the use of Levy–Student processes as a general diffusion process in various interdisciplinary applications. We explicitly provide an application in the context of modelling high-frequency price returns.

Recent literature on realized volatility suggests that the observed price process of an asset may be decomposed into two parts: the genuine (unobservable) price process and microstructure noise. In this article we present a methodology to estimate stochastic volatility by separating these components. Depending on market liquidity, the source of a move in the transaction price of an asset may be distinguished as a move in the underlying price process or as microstructure noise. To identify the weights of these components we use different (order-based and trade-based) liquidity measures to update expectations on the unobservable price process via Bayesian learning. Depending on these weights we are able to estimate stochastic volatility from noisy data.