Applications of state space models in finance

1.2 Research objectives 3
1.2 Research objectives
Although these advances spurred the interest in applying advanced time series techniques
such as the Kalman filter and Markov regime switching models in economic and
financial analysis in recent years, a transportation of these concepts from theoretical
work into applied research on a broader scale is still underdeveloped. Inspired by the
quote at the beginning of this chapter, this thesis analyzes the relative merits of selected
elaborate econometric methods to model change in the context of widely used
concepts in finance. The exploration of the dynamics of financial markets is aimed at
an improved understanding and modeling of real-world phenomena. The following three
research objectives are addressed:
1. Provide a notationally conformable introduction of Gaussian state space models,
the Markov regime switching framework and conditional heteroskedasticity models.
2. Analyze which modeling technique is best able to model and forecast time-varying
systematic beta risk as a stochastic process.
3. Evaluate the practical relevance of taking time-variation in factor sensitivities explicitly
into account.
As the different contemporaneous time series models originate from different disciplines,
very different notation and terminology is commonly employed to outline the respective
theory behind these concepts. The first objective of this thesis is to introduce the theory
of the different models at hand in a unified notational framework: linear Gaussian state
space models and the Kalman filter, the Markov regime switching framework, as well
as two of the most prominent models for time-varying volatility, namely autoregressive
conditional heteroskedasticity (ARCH) and stochastic volatility models. This will allow
the applied researcher to adopt the various concepts without having to deal with different
notation that is typical for the disciplines in which the models were originally employed.
It is intended to provide the methodology for the modeling of time-varying relationships
in a way that is as compact and intuitive as possible and as comprehensive as necessary.
The outline of the respective basic ideas and estimation procedures in Chapters 3–
5 illustrates that both Markov regime switching and stochastic volatility models are
closely related to the linear Gaussian state space framework and the Kalman filter.
The second contribution of this thesis is a systematic and comprehensive analysis of
the ability of the different techniques under consideration to model and forecast the timevarying
behavior of systematic market risk. The rationale behind starting the empirical
analysis with an application of the selected time series techniques to the single-factor
CAPM, is motivated by the fact that the CAPM beta is widely established in practice.
It is used, for example, to calculate the cost of capital, to identify mispricings and to
estimate an asset’s sensitivity to the broad market. As discussed by Yao and Gao (2004)
betas, while traditionally employed in the context of single stocks, are particularly useful
at the sector level. However, in spite of various studies dealing with the modeling of
conditional sector betas in other regions of the world, similar work in a pan-European
context, where the advancement of European integration and the introduction of a single
currency increased the importance of the sector perspective over recent years, is still