A Multivariate Non-stationary Approach for Financial Returns with Nonparametric Heteroscedasticity

58 Pages Posted: 28 Sep 2009 Last revised: 12 Jan 2013

See all articles by Marc Gürtler

Marc Gürtler

University of Braunschweig - Institute of Technology, Department of Finance

Jens‐Peter Kreiss

Technology University of Braunschweig - Department of Mathematics

Ronald Rauh

Öffentliche Versicherung Braunschweig

Date Written: September 17, 2009

Abstract

A non-stationary regression model for financial returns is examined theoretically. Volatility dynamics are modeled by nonparametric curve estimation on equidistant return vectors. We prove consistency and asymptotic normality of symmetric estimators and of one-sided estimators for variances and covariance matrices analytically, and derive remarks on kernels and bandwidths. Further attention is paid to asymmetry and heavy tails of returns, captured by an asymmetric Pearson type VII distribution for random residuals. Using a method of moments for its parameter estimation and a Student-t connection, a factor-based VaR implementation is derived. The approximation quality of the non-stationary approach is supported by simulation studies.

Keywords: non-stationary financial returns, nonparametric regression, volatility, covariance matrix, innovation modeling, asymmetric heavy-tails, distributional forecast, Value at Risk (VaR)

JEL Classification: C5, C13, C14

Suggested Citation

Gürtler, Marc and Kreiss, Jens-Peter and Rauh, Ronald, A Multivariate Non-stationary Approach for Financial Returns with Nonparametric Heteroscedasticity (September 17, 2009). Available at SSRN: https://ssrn.com/abstract=1479446 or http://dx.doi.org/10.2139/ssrn.1479446

Marc Gürtler (Contact Author)

University of Braunschweig - Institute of Technology, Department of Finance ( email )

Abt-Jerusalem-Str. 7
Braunschweig, 38106
Germany

Jens-Peter Kreiss

Technology University of Braunschweig - Department of Mathematics ( email )

Pockelsstrasse 14
Braunschweig, D–38106
Germany
(0531) 391 - 7566 (Phone)

Ronald Rauh

Öffentliche Versicherung Braunschweig ( email )

Theodor-Heuss-Str. 10
Braunschweig, 38122
Germany
+49 531 2021568 (Phone)
+49 531 202331568 (Fax)