TY - CHAP

T1 - Estimating Asymmetric Dynamic Distributions in High Dimensions

AU - Anatolyev, Stanislav

AU - Khabibullin, Renat

AU - Prokhorov, Artem

PY - 2017/3/27

Y1 - 2017/3/27

N2 - We consider estimation of dynamic joint distributions of large groups of assets. Conventional likelihood functions based on 'off-the-shelf' distributions quickly become inaccurate as the number of parameters grows. Alternatives based on a fixed number of parameters do not permit sufficient flexibility in modelling asymmetry and dependence. This chapter considers a sequential procedure, where the joint patterns of asymmetry and dependence are unrestricted, yet the method does not suffer from the curse of dimensionality encountered in non-parametric estimation. We construct a flexible multivariate distribution using tightly parameterized lower-dimensional distributions coupled by a bivariate copula. This effectively replaces a high-dimensional parameter space with many simple estimations with few parameters. We provide theoretical motivation for this estimator as a pseudo-MLE with known asymptotic properties. In an asymmetric GARCH-type application with regional stock indexes, the procedure provides excellent fit when dimensionality is moderate, and remains operational when the conventional method fails.

AB - We consider estimation of dynamic joint distributions of large groups of assets. Conventional likelihood functions based on 'off-the-shelf' distributions quickly become inaccurate as the number of parameters grows. Alternatives based on a fixed number of parameters do not permit sufficient flexibility in modelling asymmetry and dependence. This chapter considers a sequential procedure, where the joint patterns of asymmetry and dependence are unrestricted, yet the method does not suffer from the curse of dimensionality encountered in non-parametric estimation. We construct a flexible multivariate distribution using tightly parameterized lower-dimensional distributions coupled by a bivariate copula. This effectively replaces a high-dimensional parameter space with many simple estimations with few parameters. We provide theoretical motivation for this estimator as a pseudo-MLE with known asymptotic properties. In an asymmetric GARCH-type application with regional stock indexes, the procedure provides excellent fit when dimensionality is moderate, and remains operational when the conventional method fails.

KW - Asymmetric dynamic distributions

KW - Bivariate copula

KW - GARCH-type application

KW - High dimensions

KW - Parameterizations

KW - Pseudo-MLE

KW - Sequential procedure

KW - Theoretical motivation

UR - http://www.scopus.com/inward/record.url?scp=85050434920&partnerID=8YFLogxK

U2 - 10.1002/9781119288992.ch8

DO - 10.1002/9781119288992.ch8

M3 - Chapter

AN - SCOPUS:85050434920

SN - 9781119289012

SP - 169

EP - 195

BT - Assymetric Dependence in Finance

PB - Wiley-Blackwell

ER -