Multivariate GARCH Models: Software Choice and Estimation Issues

A large number of important practical tasks can be accomplished using a multivariate GARCH model. This paper examines the relatively small number of software packages that are currently available for estimating such models, in spite of their widespread use. The review focuses upon estimation issues and differences in available options for controlling the optimisation, and the review then considers an application to the estimation of optimal hedge ratios. Large differences in estimated parameters and standard errors are observed, but these are found to generate only modest differences in optimal hedge ratios and virtually indiscernible differences in model performance measures.

Evolution in cluster cores since z~1

A large fraction of the stellar mass in galaxy clusters is thought to be contained in the diffuse low surface brightness intracluster light (ICL). Being bound to the gravitational potential of the cluster rather than any individual galaxy, the ICL contains much information about the evolution of its host cluster and the interactions between the galaxies within. However due its low surface brightness it is notoriously difficult to study. We present the first detection and measurement of the flux contained in the ICL at z~1. We find that the fraction of the total cluster light contained in the ICL may have increased by factors of 2-4 since z~1, in contrast to recent findings for the lack of mass and scale size evolution found for brightest cluster galaxies. Our results suggest that late time buildup in cluster cores may occur more through stripping than merging and we discuss the implications of our results for hierarchical simulations.Comment: To appear in the Proceedings of IAU Symposium 295 - The intriguing life of massive galaxie

Augoregressive Conditional Kurtosis

This paper proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising US and UK stocks and bonds, and significant evidence in favour of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are examined, and show that conditional kurtosis appears to be positively but not significantly related to returns, and that the response of kurtosis to good and bad news is not significantly asymmetric. A multivariate model for conditional heteroscedasticity and conditional kurtosis, which can provide useful information on the co-movements between the higher moments of series, is also proposed.conditional kurtosis, GARCH, fourth moment, fat trails, student's t distribution

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling

The Properties of Brightest Cluster Galaxies in X-Ray Selected Clusters

We present the K-band Hubble diagram for 162 brightest cluster galaxies (BCGs) in X-ray selected clusters, 0.01<z<0.83. The sample incorporates that of Burke, Collins, & Mann (2000) and includes additional infrared data from the 2MASS extended source catalogue. We show that below z=0.1 the BCGs show no correlation with their environment, however, above z=0.1 BCGs in more X-ray luminous clusters are more uniform in their photometric properties. This suggests that there may be two populations of BCGs which have different evolutionary histories.Comment: 2 pages, to appear in the proceedings of the Sesto 2001 conference on tracing cosmic evolution with galaxy cluster

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper

CO2 loss by permafrost thawing implies additional emissions reductions to limit warming to 1.5 or 2°C

Large amounts of carbon are stored in the permafrost of the northern high latitude land. As permafrost degrades under a warming climate, some of this carbon will decompose and be released to the atmosphere. This positive climate-carbon feedback will reduce the natural carbon sinks and thus lower anthropogenic CO2 emissions compatible with the goals of the Paris Agreement. Simulations using an ensemble of the JULES-IMOGEN intermediate complexity climate model (including climate response and process uncertainty) and a stabilization target of 2°C, show that including the permafrost carbon pool in the model increases the land carbon emissions at stabilization by between 0.09 and 0.19 Gt C year-1 (10th to 90th percentile). These emissions are only slightly reduced to between 0.08 and 0.16 Gt C year-1 (10th to 90th percentile) when considering 1.5°C stabilization targets. This suggests that uncertainties caused by the differences in stabilization target are small compared with those associated with model parameterisation uncertainty. Inertia means that permafrost carbon loss may continue for many years after anthropogenic emissions have stabilized. Simulations suggest that between 225 and 345 Gt C (10th to 90th percentile) are in thawed permafrost and may eventually be released to the atmosphere for stabilization target of 2°C. This value is 60 to 100 Gt C less for a 1.5°C target. The inclusion of permafrost carbon will add to the demands on negative emission technologies which are already present in most low emissions scenarios

Magseal Leak Testing Device

Magnetic Seal Corp. has forged a reputable name for itself in the high performance seal industry. Despite great manufacturing practices and product quality, they strive to be even better. Their focus on product quality and cost efficiency lead them to the realization that understanding and fully characterizing porosity in their products was crucial. Due to the nature of the casting process, their magnetic housings inherently have some porosity. Despite thorough inspections upon receiving parts form vendors, porosity can, and often does appear below the surface after parts are machined. As such, a thorough understanding of how porosity effects leakage rates in their parts became essential in order to keep uphold the quality of manufactured parts and more accurately quantify their performance with respect to the standard. The Leakseekers were tasked with designing, manufacturing, and implementing a test rig capable of two things, namely isolating leakage to just the O-Ring - Seal interface, and accurately measuring any leakage past this interface. The information provided by the rig would effectively allow Magseal to more precisely determine the allowable limits of porosity on surfaces of interest, and in so-doing limit the amount of parts discarded due to a broad spectrum that determines whether a part fails inspection or not. Through the use of Financial Analysis, Engineering Analysis and tools like QDF, the team developed a modular design that, with the use of different adapters for different seals, could test a wide range of Magseal products. For optimal utility, the rig was designed with the capability of running 100 hour tests and adapting to multiple seal sizes. Heat, insulation, and pressure sub-systems were also used to ensure that the desired test parameters remained constant throughout the course of a test. An Arduino breadboard was programmed to control and regulate temperatures while an analog pressure system was employed to ensure the desired pressure. In addition to the rig, test and operation procedures, a maintenance manual, electrical system wiring diagrams, a pressure system diagram, and all final assembly CAD part and drawing files were given to the sponsor as deliverables

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric