Applications of state space models in finance

156 Conclusion and outlook
conditional regression coefficients in an indirect way. Within the versatile class of heteroskedasticity
models, many different specifications that explicitly allow for particular
empirical properties, such as fat-tailed distributions, leverage effects or volatility comovements,
are considered. As an alternative to the indirect approach, time-varying
relationships can be modeled and predicted directly: in the context of a state space
framework, the path of beta either emerges as a hidden continuous process estimated
via the Kalman filter, or as a hidden discrete process in a Markov regime switching
framework.
In the theoretical part of this thesis, the methodology to analyze the time-varying
relationship between common systematic risk factors and sector returns is introduced.
The econometric toolbox provided in Chapters 3–5 equips the reader with a range of
contemporary time series techniques of different, and often non-economic, origin: Gaussian
state space models and the Kalman filter, Markov regime switching models, and
linear and nonlinear GARCH models, and stochastic volatility models. Although choices
had to be made with respect to both breadth and depth in deciding which econometric
techniques should be employed in the course of this thesis, many features, reaching from
basic representations, estimation and path-tracking procedures to selected extensions,
are discussed. Linkages between the different concepts are emphasized: the introduction
of linear Gaussian state space model and the Kalman filter lays the ground for
the strongly connected Markov regime switching and stochastic volatility models. The
presentation of the various concepts in a unified notational framework hopefully encourages
empirical researchers with a focus on finance-related disciplines — practitioners
and academics alike — to utilize these advanced time series concepts to conduct fruitful
empirical research in a field that is characterized by daily dynamics and ongoing change.
The empirical investigation in Chapter 6 adds to the literature a comprehensive analysis
of the ability of different elaborate time series concepts to model conditional beta risk
in a pan-European context. Compared to earlier studies for other regions of the world,
the spectrum of modeling techniques employed here is expanded to also include two
Markov regime switching models, and a bivariate stochastic volatility model that is estimated
via simulation-based efficient Monte Carlo likelihood and importance sampling
techniques. A generalized random walk model is proposed to deal with heteroskedasticity
and non-normality in the context of a three-stage estimation procedure. The in-sample
results suggest that sector returns can be better explained by movements of the overall
market when betas are allowed to vary over time. Compared to standard OLS,
each time-varying approach delivers superior in-sample forecasting results. This implies
confirmation of the conditionality assumption. An evaluation of the various modeling
techniques’ ability to produce out-of-sample forecasts of conditional sector betas reveals
that the Kalman filter based random walk model offers the relatively best predictive
performance. The random walk specification is closely followed by the moving mean reverting
and the proposed generalized random walk model. Unsatisfactory out-of-sample
results are obtained by the two Markov regime switching models. It is concluded that
time-varying market beta for pan-European sectors can be best described as a stochastic
random walk process. The finding that the generalized random walk model, which
has been introduced to take volatility clustering and outliers explicitly into account,