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"Copulas (Mathematical statistics)"
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Dependence modeling
This book is a collaborative effort from three workshops held over the last three years, all involving principal contributors to the vine-copula methodology. Research and applications in vines have been growing rapidly and there is now a growing need to collate basic results, and standardize terminology and methods. Specifically, this handbook will (1) trace historical developments, standardizing notation and terminology, (2) summarize results on bivariate copulae, (3) summarize results for regular vines, and (4) give an overview of its applications. In addition, many of these results are new and not readily available in any existing journals. New research directions are also discussed.
eBook
Simulating copulas : stochastic models, sampling algorithms, and applications
This tome provides the reader with a background on simulating copulas and multivariate distribution in general. It unifies the scattered literature on the simulation of various families of copulas as well as on different construction principles.
Book
An SIR epidemic on a weighted network
We introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible–Infectious–Recovered epidemic using both Reed–Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction number R 0 , the probability of a major outbreak , and the relative final size of a major outbreak . Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical constructs and empirical network data. In addition, bivariate standard normal copulas are used to model the dependence between the degrees of the two edge types, allowing for modeling the correlation between edge types over a wide range. Among the results are that the weighted graph produces much richer results than the unweighted graph. Also, while R 0 always increases with increasing correlation between the two degrees, this is not necessarily true for the probability of a major outbreak nor for the relative final size of a major outbreak. When using copulas we see that these can produce results that are similar to those of the empirical degree distributions, indicating that in some cases a copula is a viable alternative to using the full empirical data.
Journal Article
Meteorological drought in Northland, New Zealand
Meteorological drought, or a prolonged period of below average precipitation, is a significant and recurring hazard in Northland, where eight droughts, all having severe negative impacts, have been recorded since 1900. The cause of drought is usually the persistence of slow-moving or blocking high-pressure systems over Northland during the summer seasons. The reasons for this behaviour and the links between severe drought occurrence and natural climate fluctuations caused by the El Niño-Southern Oscillation, the Interdecadal Pacific Oscillation and the Southern Annular Mode are poorly understood. An analysis of meteorological droughts, characterised by severity, duration, and frequency (return period) is undertaken for the period 1893–2018. Severity is measured by the Standardized Precipitation Index (SPI) and severity-duration-frequency relationships are described for 298 Northland rain gauge sites using copulas.
The worst year in terms of monthly SPI values was 1993 when nearly 25% of all sites were affected by drought. Based on severity alone the worst drought (severity = 21.19 at Whangārei Harbour) occurred in 1987 and had a duration of 10 months and the three worst drought years were (in order) 1987, 1913 and 1990. Based on duration alone the worst drought occurred in 1993 at Topuni with a duration of 16 months and the three worst drought years were (in order) 1993, 1913 and 1986.
Statistical tests of SPI values showed no consistent and significant temporal trend in drought occurrence in the 125-year period. Attempts at contouring and clustering demonstrated that SPI relationships are not spatially dependent, implying that there are no specific drought-prone areas and that drought may occur at any locality and time in Northland (given the appropriate synoptic conditions).
Further work is needed to improve climatological understanding of drought occurrence, along with continued monitoring of drought conditions. Use of multivariate copulas, including extra variables such as minimum SPI values and spatial extent, should provide a more comprehensive description of drought in Northland.
Journal Article
Anticipating correlations
Financial markets respond to information virtually instantaneously. Each new piece of information influences the prices of assets and their correlations with each other, and as the system rapidly changes, so too do correlation forecasts. This fast-evolving environment presents econometricians with the challenge of forecasting dynamic correlations, which are essential inputs to risk measurement, portfolio allocation, derivative pricing, and many other critical financial activities. In Anticipating Correlations, Nobel Prize-winning economist Robert Engle introduces an important new method for estimating correlations for large systems of assets: Dynamic Conditional Correlation (DCC). Engle demonstrates the role of correlations in financial decision making, and addresses the economic underpinnings and theoretical properties of correlations and their relation to other measures of dependence. He compares DCC with other correlation estimators such as historical correlation, exponential smoothing, and multivariate GARCH, and he presents a range of important applications of DCC. Engle presents the asymmetric model and illustrates it using a multicountry equity and bond return model. He introduces the new FACTOR DCC model that blends factor models with the DCC to produce a model with the best features of both, and illustrates it using an array of U.S. large-cap equities. Engle shows how overinvestment in collateralized debt obligations, or CDOs, lies at the heart of the subprime mortgage crisis--and how the correlation models in this book could have foreseen the risks. A technical chapter of econometric results also is included.
eBook
Introduction to Bayesian estimation and copula models of dependence
Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence.
eBook
Dynamic copula methods in finance
The latest tools and techniques for pricing and risk management This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications.
eBook