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

A robust bootstrap approach to the Hausman test in stationary panel data models

In panel data econometrics the Hausman test is of central importance to select an e?cient estimator of the models' slope parameters. When testing the null hypothesis of no correlation between unobserved heterogeneity and observable explanatory variables by means of the Hausman test model disturbances are typically assumed to be independent and identically distributed over the time and the cross section dimension. The test statistic lacks pivotalness in case the iid assumption is violated. GLS based variants of the test statistic are suitable to overcome the impact of nuisance parameters on the asymptotic distribution of the Hausman statistic. Such test statistics, however, also build upon strong homogeneity restrictions that might not be met by empirical data. We propose a bootstrap approach to specification testing in panel data models which is robust under cross sectional or time heteroskedasticity and inhomogeneous patterns of serial correlation. A Monte Carlo study shows that in small samples the bootstrap approach outperforms inference based on critical values that are taken from a X?-distribution. --Hausman test,random effects model,wild bootstrap,heteroskedasticity

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

Low mortgage rates and securitization: A distinct perspective on the U.S. housing boom

Copyright © 2018 The Authors. In this paper, we analyse the impacts of low interest rates and lax underwriting standards on the US housing boom around the beginning of the new millennium. We suggest a time-varying mean of the log price-to-rent ratio (PtR) to capture the persistent changes in housing prices. We show that the increasing latent trend in the PtR was significantly affected by the increased securitization of residential mortgage loans and decreasing interest rates, with the former effect being about three times larger than the latter. In the absence of securitization, negative interest rates would have been needed to reproduce an equally large housing boom since 2003.German Research Foundation (HE2188/8-1); Fritz Thyssen Stiftung (Az.10.08.1.088)

Labelled drug-related public expenditure in relation to gross domestic product (gdp) in Europe: A luxury good?

"Labelled drug-related public expenditure" is the direct expenditure explicitly labelled as related to illicit drugs by the general government of the state. As part of the reporting exercise corresponding to 2005, the European Monitoring Centre for Drugs and Drug Addiction's network of national focal points set up in the 27 European Union (EU) Member States, Norway, and the candidates countries to the EU, were requested to identify labelled drug-related public expenditure, at the country level. This was reported by 10 countries categorised according to the functions of government, amounting to a total of EUR 2.17 billion. Overall, the highest proportion of this total came within the government functions of Health (66%), and Public Order and Safety (POS) (20%). By country, the average share of GDP was 0.023% for Health, and 0.013% for POS. However, these shares varied considerably across countries, ranging from 0.00033% in Slovakia, up to 0.053% of GDP in Ireland in the case of Health, and from 0.003% in Portugal, to 0.02% in the UK, in the case of POS; almost a 161-fold difference between the highest and the lowest countries for Health, and a 6-fold difference for POS. Why do Ireland and the UK spend so much in Health and POS, or Slovakia and Portugal so little, in GDP terms? To respond to this question and to make a comprehensive assessment of drug-related public expenditure across countries, this study compared Health and POS spending and GDP in the 10 reporting countries. Results found suggest GDP to be a major determinant of the Health and POS drug-related public expenditures of a country. Labelled drug-related public expenditure showed a positive association with the GDP across the countries considered: r = 0.81 in the case of Health, and r = 0.91 for POS. The percentage change in Health and POS expenditures due to a one percent increase in GDP (the income elasticity of demand) was estimated to be 1.78% and 1.23% respectively. Being highly income elastic, Health and POS expenditures can be considered luxury goods; as a nation becomes wealthier it openly spends proportionately more on drug-related health and public order and safety interventions