A Multivariate Non-stationary Approach for Financial Returns with Nonparametric Heteroscedasticity
58 Pages Posted: 28 Sep 2009 Last revised: 12 Jan 2013
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: Suggested Citation
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