Applications of state space models in finance

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16 2 Some stylized facts of weekly sector return series throughout this thesis conditionality is dealt with by employing time series models. As it is typically not possible to model all distributional and temporal properties of return series simultaneously, different models are typically used to capture different empirical regularities (cf. Ghysels et al. 1996). Time-varying relationships can be constructed either directly or indirectly. The direct approach will be implemented by employing a state space framework, where beta can be allowed to emerge either as a continuous process estimated via the Kalman filter, or as a discrete process in a Markov regime switching framework. Alternatively, indirect estimates of conditional sensitivities can be derived by capturing the underlying conditional variance and covariance components by a conditional heteroskedasticity model. Before applying these different concepts to analyze the time-varying relationship between macroeconomics, fundamentals and pan-European industry portfolios, the theoretical groundwork is made available in the subsequent theoretical part of this thesis.
Chapter 3 Linear Gaussian state space models and the Kalman filter This chapter introduces the class of linear Gaussian state space models from the classical perspective of maximum likelihood estimation. The first section outlines the basic ideas behind state space modeling. Section 3.2 presents the general state space form of a dynamic system. Section 3.3 develops the Kalman filter and smoother, the basic tools to estimate models in state space form. Section 3.4 describes maximum likelihood estimation procedures for the unknown parameters. Section 3.5 extends the general state space model to allow for the incorporation of explanatory variables with constant as well as time-varying parameters. Model diagnostics and measures to assess the goodness of fit are described in Section 3.6. The chapter finishes with an illustration of how to specify state space models using the software package SsfPack. 3.1 Basic ideas of state space modeling The state space form of a dynamic system with unobserved components is a very powerful and flexible instrument. A wide range of all linear and many nonlinear time series models can be handled, including regression models with changing coefficients, autoregressive integrated moving average (ARIMA) models and unobserved component models. A state space model consists of a state equation and an observation equation. While the state equation formulates the dynamics of the state variables, the observation equation relates the observed variables to the unobserved state vector. The state vector can contain trend, seasonal, cycle and regression components plus an error term. Models that relate the observations over time to different components, which are usually modeled as individual random walks, are referred to as structural time series models. The stochastic behavior of the state variable, its relationship to the data and the covariance structure of the errors depend on parameters that are also generally unknown. The state variable and the parameters have to be estimated from the data. Maximum likelihood estimates of the parameters can be obtained by applying the Kalman filter. Named after Kalman (1960, 1963) the Kalman filter is a recursive algorithm that computes estimates for the unobserved components at time t, based on the available information at the same date.
Page 1: Sascha Mergner Applications of Stat
Page 4 and 5: erschienen im Universitätsverlag G
Page 6 and 7: Bibliographische Information der De
Page 9 and 10: Contents List of figures . . . . .
Page 11 and 12: Contents ix 4.5 Model selection and
Page 13: Contents xi 7.5 Concluding remarks
Page 16 and 17: xiv List of figures 6.14 Histograms
Page 19: Notation and conventions The outlin
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Page 29: Preface The work on this book began
Page 33 and 34: Chapter 1 Introduction “Economist
Page 35 and 36: 1.2 Research objectives 3 1.2 Resea
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Page 77 and 78: 4.1 Basic concepts 45 R t (%) 20 10
Page 79 and 80: 4.1 Basic concepts 47 probability d
Page 81 and 82: 4.3 Parameter estimation 49 X 1 X 2
Page 83 and 84: 4.3 Parameter estimation 51 4.3.2.1
Page 85 and 86: 4.4 Forecasting and decoding 53 4.4
Page 87 and 88: 4.4 Forecasting and decoding 55 mod
Page 89 and 90: Chapter 5 Conditional heteroskedast
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Page 97 and 98: 5.2 Stochastic volatility 65 or the
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5.2 Stochastic volatility 67 5.2.1.
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5.2 Stochastic volatility 69 likeli
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5.2 Stochastic volatility 71 linear
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5.2 Stochastic volatility 73 3. An
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5.3 Multivariate conditional hetero
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84 6 Time-varying market beta risk
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Chapter 7 A Kalman filter based con
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7.1 Factor modeling 125 uncondition
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7.1 Factor modeling 127 predictabil
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7.1 Factor modeling 129 usefulness,
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7.2 Specification of a conditional
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7.3 The risk factors 133 Table 7.1:
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7.3 The risk factors 135 introduced
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7.3 The risk factors 137 auxiliary
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7.4 Empirical results 139 Table 7.4
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7.4 Empirical results 141 are consi
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7.4 Empirical results 145 β TS 0.4
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7.4 Empirical results 153 cumulativ
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Chapter 8 Conclusion and outlook Th
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Conclusion and outlook 157 cannot o
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Appendix A Brief review of asset pr
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A.3 Alternative asset pricing model
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Appendix B Figures
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Figures 165 β t β t β t 2.0 1.5
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Appendix C Tables
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Tables 179 Table C.1 — continued
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Tables 181 Table C.3: In-sample mea
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Tables 183 Table C.5: Out-of-sample
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Tables 185 Table C.7: Parameter est
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Tables 187 Table C.7 — continued
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Tables 189 Table C.8: Out-of-sample
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References Abell, J. D. and T. M. K
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References 193 Bulla, J. (2006). Ap
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References 195 Fabozzi, F. J. and J
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References 197 Harvey, A. C., E. Ru
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References 199 Lie, F., R. Brooks,
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References 201 Shephard, N. (1993).
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State space models play a key role
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