Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian and show in a simulation study that they clearly outperform numerical methods. As an example, we use the popular BEKK-GARCH model, for which wederive first and second order derivatives.multivariate GARCH models;quasi maximum likelihood

Testing for causality in variance using multivariate GARCH models

Tests of causality in variance in multiple time serieshave been proposed recently, based on residuals of estimatedunivariate models. Although such tests are applied frequentlylittle is known about their power properties. In this paper weshow that a convenient alternative to residual based testing is tospecify a multivariate volatility model, such as multivariateGARCH (or BEKK), and construct a Wald test on noncausality invariance. We compare both approaches to testing causality invariance in terms of asymptotic and finite sample properties. TheWald test is shown to have superior power properties under asequence of local alternatives. Furthermore, we show by simulationthat the Wald test is quite robust to misspecification of theorder of the BEKK model, but that empirical power decreasessubstantially when asymmetries in volatility are ignored.causality;local power;multivariate volatility

Testing for vector autoregressive dynamics under heteroskedasticity

In this paper we introduce a bootstrap procedure to test parameterrestrictions in vector autoregressive models which is robust incases of conditionally heteroskedastic error terms. The adoptedwild bootstrap method does not require any parametricspecification of the volatility process and takes contemporaneouserror correlation implicitly into account. Via a Monte Carloinvestigation empirical size and power properties of the newmethod are illustrated. We compare the bootstrap approach withstandard procedures either ignoring heteroskedasticity or adoptinga heteroskedasticity consistent estimation of the relevantcovariance matrices in the spirit of the White correction. Interms of empirical size the proposed method clearly outperformscompeting approaches without paying any price in terms of sizeadjusted power. We apply the alternative tests to investigate thepotential of causal relationships linking daily prices of naturalgas and crude oil. Unlike standard inference ignoring time varyingerror variances, heteroskedasticity consistent test procedures donot deliver any evidence in favor of short run causality betweenthe two series.Energy markets;Causality;Bootstrap;Heteroskededasticity;Hypothesis testing;Vector autoregression

Evolution of Feedback Loops in Oscillatory Systems

Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved. Based on published models from the mitotic cycle in embryogenesis, we build a few case studies. Using a simple core architecture (transcription, phosphorylation and degradation), we define oscillatory models having either one positive feedback or one negative feedback, or both loops. With these models, we address the following questions about evolvability: could a system evolve from a simple model to a more complex one with a continuous transition in the parameter space? How do new feedback loops emerge without disrupting the proper function of the system? Our results show that progressive formation of a second feedback loop is possible without disturbing existing oscillatory behavior. For this process, the parameters of the system have to change during evolution to maintain predefined properties of oscillations like period and amplitude.Comment: Proceedings of the 2009 FOSBE conference in Denver, CO, USA. 4 page

Spatial cytoskeleton organization supports targeted intracellular transport

The efficiency of intracellular cargo transport from specific source to target locations is strongly dependent upon molecular motor-assisted motion along the cytoskeleton. Radial transport along microtubules and lateral transport along the filaments of the actin cortex underneath the cell membrane are characteristic for cells with a centrosome. The interplay between the specific cytoskeleton organization and the motor performance realizes a spatially inhomogeneous intermittent search strategy. In order to analyze the efficiency of such intracellular search strategies we formulate a random velocity model with intermittent arrest states. We evaluate efficiency in terms of mean first passage times for three different, frequently encountered intracellular transport tasks: i) the narrow escape problem, which emerges during cargo transport to a synapse or other specific region of the cell membrane, ii) the reaction problem, which considers the binding time of two particles within the cell, and iii) the reaction-escape problem, which arises when cargo must be released at a synapse only after pairing with another particle. Our results indicate that cells are able to realize efficient search strategies for various intracellular transport tasks economically through a spatial cytoskeleton organization that involves only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments

Testing for vector autoregressive dynamics under heteroskedasticity

In this paper we introduce a bootstrap procedure to test parameter restrictions in vector autoregressive models which is robust in cases of conditionally heteroskedastic error terms. The adopted wild bootstrap method does not require any parametric specification of the volatility process and takes contemporaneous error correlation implicitly into account. Via a Monte Carlo investigation empirical size and power properties of the new method are illustrated. We compare the bootstrap approach with standard procedures either ignoring heteroskedasticity or adopting a heteroskedasticity consistent estimation of the relevant covariance matrices in the spirit of the White correction. In terms of empirical size the proposed method clearly outperforms competing approaches without paying any price in terms of size adjusted power. We apply the alternative tests to investigate the potential of causal relationships linking daily prices of natural gas and crude oil. Unlike standard inference ignoring time varying error variances, heteroskedasticity consistent test procedures do not deliver any evidence in favor of short run causality between the two series

Testing for causality in variance using multivariate GARCH models

Tests of causality in variance in multiple time series have been proposed recently, based on residuals of estimated univariate models. Although such tests are applied frequently little is known about their power properties. In this paper we show that a convenient alternative to residual based testing is to specify a multivariate volatility model, such as multivariate GARCH (or BEKK), and construct a Wald test on noncausality in variance. We compare both approaches to testing causality in variance in terms of asymptotic and finite sample properties. The Wald test is shown to have superior power properties under a sequence of local alternatives. Furthermore, we show by simulation that the Wald test is quite robust to misspecification of the order of the BEKK model, but that empirical power decreases substantially when asymmetries in volatility are ignored

Analytical quasi maximum likelihood inference in multivariate volatility models

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian and show in a simulation study that they clearly outperform numerical methods. As an example, we use the popular BEKK-GARCH model, for which we derive first and second order derivatives

A Model Partnership: The American Heart Association and Higher Education

The rapid growth of the nonbusiness, nongovernmental, third sector\u27\u27 during the past fifteen years has produced, de facto, a new type of professional manager. The small charities which once employed only a few community organizers and a secretary, now employ one out of every six professionals in the United States (Drucker, 1982)