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.
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