A non-stationary approach for financial returns with nonparametric heteroscedasticity

Marc Gürtler, Jens-Peter Kreiss and Ronald Rauh

No IF31V2, Working Papers from Technische Universität Braunschweig, Institute of Finance

Abstract: A non-stationary regression model for financial returns is examined theoretically in this paper. Volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric curve estimation on equidistant centered returns. We prove consistency and asymptotic normality of a symmetric variance estimator and of a one-sided variance estimator analytically, and derive remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, implemented by an asymmetric version of the Pearson type VII distribution for random innovations. By providing a method of moments for its parameter estimation and a connection to the Student-t distribution we offer the framework for a factor-based VaR approach. The approximation quality of the non-stationary model is supported by simulation studies.

Keywords: heteroscedastic asset returns; non-stationarity; nonparametric regression; volatility; innovation modelling; asymmetric heavy-tails; distributional forecast; Value at Risk (VaR) (search for similar items in EconPapers)
JEL-codes: C14 C51 C52 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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