The book addresses the problem of a time-varying unconditional variance of return processes utilizing a spline function. The knots of the spline functions are estimated as free parameters within a joined estimation process together with the parameters of the mean, the conditional variance and the spline function. With the help of this method, the knots are placed in regions where the unconditional variance is not smooth. The results are tested within an extensive simulation study and an empirical study employing the S&P500 index.

Autorentext

The dissertation was written at the Chair of Applied Statistics and Methods of Empirical Social Research at the Faculty of Economics and Business Administration of the FernUniversität in Hagen. From 2021 Oliver Old researched in the field of applied statistics, machine learning and data science at two EU-Horizon projects at the Department of Anesthesiology, Intensive Care and Pain Therapy at the University Hospital Frankfurt.

Inhalt
Introduction.- Financial time series.- Smoothing long term volatility.- 4 Free-knot spline-GARCH model.- Simulation study.- Empirical study.- Conclusion.