Applications of state space models in finance

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Contents List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Notation and conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Used abbreviations and symbols . . . . . . . . . . . . . . . . . . . . . . . . . xix Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix 1 Introduction 1 1.1 The modeling of change . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Some stylized facts of weekly sector return series 7 2.1 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Empirical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Thick tails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Volatility clustering . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.3 Leverage effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.4 Volatility co-movements . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Linear Gaussian state space models and the Kalman filter 17 3.1 Basic ideas of state space modeling . . . . . . . . . . . . . . . . . . . . . 17 3.2 The state space form of a dynamic system . . . . . . . . . . . . . . . . . 19 3.3 The Kalman filter and smoother . . . . . . . . . . . . . . . . . . . . . . 20 3.3.1 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.1.1 The general form of the Kalman filter . . . . . . . . . . 21 3.3.1.2 The steady-state Kalman filter . . . . . . . . . . . . . . 22 3.3.2 State smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.3 Disturbance smoothing . . . . . . . . . . . . . . . . . . . . . . . 23 3.3.3.1 Disturbance smoothing recursion . . . . . . . . . . . . . 23 3.3.3.2 Fast state smoothing . . . . . . . . . . . . . . . . . . . 24 3.3.4 Missing observations . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.5 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.6 Initialization of filter and smoother . . . . . . . . . . . . . . . . . 25
Page 1: Sascha Mergner Applications of Stat
Page 4 and 5: erschienen im Universitätsverlag G
Page 6 and 7: Bibliographische Information der De
Page 10 and 11: viii Contents 3.3.7 The Kalman filt
Page 12 and 13: x Contents 6.2.3.2 The mean reverti
Page 15 and 16: List of figures 2.1 Hierarchical cl
Page 17: List of tables 2.1 The DJ Stoxx sec
Page 21 and 22: Used abbreviations and symbols Abbr
Page 23 and 24: Used abbreviations and symbols xxi
Page 25 and 26: Used abbreviations and symbols xxii
Page 27: Used abbreviations and symbols xxv
Page 31: Acknowledgements I sincerely thank
Page 34 and 35: 2 1 Introduction sensitivities in f
Page 36 and 37: 4 1 Introduction missing. Chapter 6
Page 39 and 40: Chapter 2 Some stylized facts of we
Page 41 and 42: 2.1 The data 9 Table 2.1: The DJ St
Page 43 and 44: 2.2 Empirical properties 11 p t R t
Page 45 and 46: 2.2 Empirical properties 13 2.2.2 V
Page 47 and 48: 2.3 Implications 15 CUSUMSQ test 1.
Page 49 and 50: Chapter 3 Linear Gaussian state spa
Page 51 and 52: 3.2 The state space form of a dynam
Page 53 and 54: 3.3 The Kalman filter and smoother
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3.4 Maximum likelihood estimation 2
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3.5 Introduction of explanatory var
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3.5 Introduction of explanatory var
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3.6 Model diagnostics 37 3.6.1 Resi
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3.6 Model diagnostics 39 3.6.2.2 Co
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3.7 Illustration: How to specify th
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44 4 Markov regime switching who em
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46 4 Markov regime switching based
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48 4 Markov regime switching While
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50 4 Markov regime switching 4.3.1
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52 4 Markov regime switching Taking
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54 4 Markov regime switching such t
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56 4 Markov regime switching 4.5 Mo
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58 5 Conditional heteroskedasticity
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Chapter 6 Time-varying market beta
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6.1 The unconditional beta in the C
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6.2 Modeling conditional betas 87 v
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6.2 Modeling conditional betas 89 T
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6.2 Modeling conditional betas 91 R
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6.2 Modeling conditional betas 95 c
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6.2 Modeling conditional betas 101
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6.3 Analysis of empirical results 1
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6.4 Concluding remarks 119 of 150 w
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6.4 Concluding remarks 121 be furth
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124 7 A Kalman filter based conditi
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156 Conclusion and outlook conditio
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158 Conclusion and outlook conduct
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160 Appendix A A.2 The consumption-
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162 Appendix A The APT, introduced
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164 Appendix B β t β t β t 2.0 1
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176 Appendix B cumulative return (%
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178 Appendix C Table C.1: Compariso
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180 Appendix C Table C.2: In-sample
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182 Appendix C Table C.4: Out-of-sa
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184 Appendix C Table C.6: Out-of-sa
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186 Appendix C Table C.7 — contin
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188 Appendix C Table C.7 — contin
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190 Appendix C Table C.9: Fama-MacB
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192 References Baum, L. E. and T. P
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194 References de Jong, P. (1991).
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196 References Giannopoulos, K. (19
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198 References Keim, D. B. and R. F
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200 References Pagan, A. R. (1996).
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202 References Wells, C. (1994). Va
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Applications of state space models in finance

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