Locally Time Homogeneous Time Series Modelling

Modelling particular features (“stylized facts”) of financial time series such as volatility clustering, heavy tails, asymmetry, etc. is an important task arising in financial engineering. For instance, attempts to model volatility clustering, i.e. the tendency of volatility jumps to appear in groups followed by periods of stability, led to the development of conditional heteroskedastic (CH) models including ARCH by Engle (1982) and GARCH by Bollerslev (1986) as well as their derivatives. The main idea underlying the mentioned methods is that volatility clustering can be modelled globally by a stationary process.

The chapter is organized as follows. Section 17.2 is devoted to the formulation of the problem and theoretical introduction. Section 17.3 describes the methods under comparison. In Section 17.4 the procedure for obtaining critical values, essential parameters of the procedures, is given. Section 17.5 shows the application of the adaptive methods to the computation of the value-at-risk.