Simon Thinggaard Hetland defends his PhD thesis

Candidate

Simon Thinggaard Hetland

Title: "Dynamic Conditional Eigenvalues"

Time and place: 29 June 2021 at 15:30 in CSS 26.2.21/ZOOM.

Link to attend the defense by ZOOM follows here: :  https://ucph-ku.zoom.us/j/9536476672

An electronic copy of the thesis can be obtained here: charlotte.jespersen@econ.ku.dk

Assessment Committee

• Professor Mette Ejrnæs, Department of Economics, University of Copenhagen, Denmark (chairman)
• Professor Nikolaus Hautsch, Universität Wien, Austria
• Professor Giuseppe Cavaliere, ALMA MATER STUDIORUM - Università di Bologna, Italy
  
  

Abstract
In this thesis, we study a class of multivariate generalized autoregressive heteroskedasticity (GARCH) models, denoted the Dynamic Conditional Eigenvalue GARCH model. Multivariate GARCH models are useful for estimating and filtering time varying (co-)variances, which are used e.g. in empirical asset pricing, Markovitz-type portfolio optimization and value-at-risk estimation. GARCH models have long been a staple in empirical finance and financial econometrics. This thesis contains three self-contained chapters on the Dynamic Conditional Eigenvalue GARCH, covering large-sample properties and bootstrap-based inference.

In the first chapter, The Dynamic Conditional Eigenvalue GARCH Model, we introduce the Dynamic Conditional Eigenvalue GARCH class of models, where the eigenvalues of the conditional covariance matrix are time varying. We provide new results on asymptotic theory for the Gaussian quasi-maximum likelihood estimator, and for testing of reduced rank of the (G)ARCH loading matrices of the time-varying eigenvalues. The theory is applied to US data, where we find that the eigenvalue structure can be reduced similar to testing for the number in factors in volatility models. This chapter is jointly written with Anders Rahbek and Rasmus Søndergaard Pedersen.

The second chapter, Spectral Targeting Estimation of Dynamic Conditional Eigenvalue GARCH Models, investigates a two-step estimator of the Dynamic Conditional Eigenvalue GARCH model, combining (eigenvalue and -vector) targeting estimation with stepwise (univariate) estimation. This estimator is denoted the ``spectral targeting estimator''. We find that the estimator is consistent under finite second order moments, while asymptotic normality holds under finite fourth order moments. The estimator is especially well suited for modeling larger portfolios: we compare the empirical performance of the spectral targeting estimator to that of the quasi-maximum likelihood estimator for five portfolios of 25 assets. The spectral targeting estimator dominates in terms of computational complexity, being up to 57 times faster in estimation, while both estimators produce similar out-of-sample forecasts, indicating that the spectral targeting estimator is well suited for high-dimensional empirical applications.

In the third and final chapter, Bootstrap-Based Inference and Testing in Multivariate Dynamic Conditional Eigenvalue GARCH Models, we study fixed-design bootstrap for quasi-maximum likelihood estimation of multivariate GARCH processes. We show, under fairly mild conditions, that the bootstrap Wald test statistic is consistent, conditional on the original data. The theoretically investigated fixed-design bootstrap is contrasted to a recursive bootstrap, and the asymptotic test statistic. Through Monte Carlo simulations, we find evidence that the fixed-design bootstrap is superior to the recursive bootstrap and the asymptotic test in small samples. In larger samples, both bootstrap designs and the asymptotic test share properties, as expected from the asymptotic theory. An empirical application illustrates the empirical merits of the bootstrap in multivariate GARCH models. The appealing theoretical properties, along with the excellent finite sample properties, suggest that the fixed-design bootstrap is an important tool for small sample inference in multivariate GARCH models.