Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model (Gabler Theses)

Foreword
Acknowledgements
Contents
List of Figures
List of Tables
List of Abbreviations
List of Symbols
1 Introduction
	1.1 Motivation
	1.2 Problem statement
	1.3 Outline of the thesis
2 Financial time series
	2.1 Definitions and properties
	2.2 Stylized facts
	2.3 Model specification
	2.4 Univariate GARCH models
	2.5 Long-range dependence and structural breaks
3 Smoothing long term volatility
	3.1 Multiplicative decomposition of the conditional variance function
	3.2 Spline functions
		3.2.1 Truncated power spline function
		3.2.2 B-spline functions
	3.3 Model review
		3.3.1 Spline volatility models
		3.3.2 Spline-GARCH model
		3.3.3 B-spline-GARCH model
		3.3.4 P-spline GARCH model
4 Free-knot spline-GARCH model
	4.1 Optimization
	4.2 Estimation methods
		4.2.1 Least-squares
		4.2.2 Least-squares with free-knots
		4.2.3 Jupp transformation
		4.2.4 Quasi-maximum-likelihood
	4.3 Model selection
	4.4 Forecast evaluation
	4.5 Starting vector
5 Simulation study
	5.1 Previous studies
	5.2 Simulation setup
		5.2.1 Data generating process
		5.2.2 Computational aspects
		5.2.3 Sample statistics
		5.2.4 Asymptotic statistics
		5.2.5 Specification
		5.2.6 Starting vectors
	5.3 Model selection
	5.4 Finite sample properties
6 Empirical study
	6.1 Previous studies
	6.2 In-sample analysis
	6.3 Out-of-sample forecast
7 Conclusion
	7.1 Research problems and contributions
	7.2 Research questions
	7.3 Limitations and future research
	7.4 Concluding remarks
References
Appendices
A Standardized Student’s t-distribution
B Derivatives
	B.1 Free-knot spline-GARCH model
	B.2 P-spline-GARCH model
C Tables
	C.1 Simulation study: knots
	C.2 Simulation study: Finite sample properties
	C.3 Empirical study
D Figures
	D.1 Simulation study: distribution of knot selection
	D.2 Simulation study: asymptotic distribution estimators
	D.3 Emprical study