Workshop on advances in time series econometrics

Programme 

Karim Abadir, Imperial College London 

Link of moments before and after transformations, with an application to resampling from fat-tailed distributions

Abstract: Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms are taken. We illustrate one of the implications of our method by providing accurate naive bootstrap confidence intervals for the mean of a fat-tailed distribution with an infinite variance, in which case currently-available bootstrap methods are asymptotically invalid and unreliable in finite sample. (Joint with Adriana Cornea-Madeira)

Paolo Paruolo, JRC Ispra  

Likelihood ratio tests of restrictions on common-trends loading matrices in I(2) VAR systems

Abstract: Likelihood Ratio tests of over-identifying restrictions on the common-trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common-trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are reviewed, and asymptotic properties discussed. An illustration is provided based on the analysis of the PPP and UIP between Switzerland and the US. (Joint with H. Peter Boswijk)

Michael Wolf, University of Zurich

Large Dynamic Covariance Matrices

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper aims to marry these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices. (Joint with Robert Engle and Olivier Ledoit)

Organisers

Giuseppe Cavaliere and Alessandra Luati