Applications of state space models in finance

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xiv List of figures 6.14 Histograms of Spearman’s out-of-sample rank correlations for the random walk, the moving mean reverting and the generalized random walk model (520 samples). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.1 V GR factor loadings for Technology and Food & Beverages. . . . . . . . 144 7.2 SIZ factor loadings for Industrials and Healthcare. . . . . . . . . . . . . 144 7.3 T S factor loadings for Automobiles and Insurance. . . . . . . . . . . . . 145 7.4 OIL and V GR betas for the Oil & Gas sector. . . . . . . . . . . . . . . 145 7.5 F X factor loadings for Utilities and Industrials. . . . . . . . . . . . . . . 146 7.6 (a) Cumulative quintile and (b) spread returns for the KF portfolios. . 152 7.7 (a) Cumulative KF spread return and (b) cumulative spread returns of the alternative portfolios relative to the KF based portfolios. . . . . . . 153 B.1 t-GARCH and stochastic volatility conditional betas. . . . . . . . . . . . 164 B.2 Random walk and mean reverting conditional betas. . . . . . . . . . . . 167 B.3 Moving mean reverting and generalized random walk conditional betas. 170 B.4 Markov switching and Markov switching market conditional betas. . . . 173 B.5 Cumulative quintile returns and spread returns for the RLS, RR5 and RR1 portfolios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
List of tables 2.1 The DJ Stoxx sector classification. . . . . . . . . . . . . . . . . . . . . 9 2.2 Summary statistics of weekly excess returns. . . . . . . . . . . . . . . . . 12 6.1 OLS estimates of the excess market model. . . . . . . . . . . . . . . . . 85 6.2 Testing for asymmetric ARCH effects. . . . . . . . . . . . . . . . . . . . 89 6.3 Comparison of different GARCH(1,1) specifications. . . . . . . . . . . . 90 6.4 Parameter estimates for t-GARCH(1,1) models. . . . . . . . . . . . . . . 91 6.5 Parameter estimates for stochastic volatility models. . . . . . . . . . . . 93 6.6 Parameter estimates for Kalman filter models. . . . . . . . . . . . . . . . 97 6.7 Parameter estimates for Markov switching models. . . . . . . . . . . . . 108 6.8 Information criteria of out-of-sample rank correlations. . . . . . . . . . . 118 6.9 Average out-of-sample MAE and MSE across sectors (520 samples). . . 119 7.1 Glossary and definition of risk factors. . . . . . . . . . . . . . . . . . . . 133 7.2 Correlations between the DJ Stoxx Broad index and the chosen macroeconomic and fundamental risk factors (8.1.1992–2.2.2005). . . . . . . . . 137 7.3 Parameter estimates for auxiliary regression (9.1.1991–2.2.2005). . . . . 138 7.4 Summary statistics for the set of risk factors (8.1.1992–2.2.2005). . . . . 139 7.5 Risk factor cross-correlations. . . . . . . . . . . . . . . . . . . . . . . . . 140 7.6 Parameter estimates for multifactor Kalman filter models. . . . . . . . . 143 7.7 Average out-of-sample errors across sectors for multiple factor models. . 147 7.8 Fama-MacBeth regression results I. . . . . . . . . . . . . . . . . . . . . . 149 7.9 Summary results of simple backtests. . . . . . . . . . . . . . . . . . . . . 151 7.10 Summary results of natural backtests. . . . . . . . . . . . . . . . . . . . 152 C.1 Comparison of OLS betas and various conditional beta series. . . . . . . 178 C.2 In-sample mean absolute errors. . . . . . . . . . . . . . . . . . . . . . . . 180 C.3 In-sample mean squared errors. . . . . . . . . . . . . . . . . . . . . . . . 181 C.4 Out-of-sample mean absolute errors (100 samples). . . . . . . . . . . . . 182 C.5 Out-of-sample mean squared errors (100 samples). . . . . . . . . . . . . 183 C.6 Out-of-sample mean absolute and squared errors (520 samples). . . . . . 184 C.7 Parameter estimates for least squares based multifactor models. . . . . . 185 C.8 Out-of-sample errors for multiple factor models. . . . . . . . . . . . . . . 189 C.9 Fama-MacBeth regression results II. . . . . . . . . . . . . . . . . . . . . 190
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 19: Notation and conventions The outlin
Page 22 and 23: xx Used abbreviations and symbols L
Page 24 and 25: xxii Used abbreviations and symbols
Page 26 and 27: xxiv Used abbreviations and symbols
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
Page 37: 1.3 Organization of the thesis 5 to
Page 40 and 41: 8 2 Some stylized facts of weekly s
Page 42 and 43: 10 2 Some stylized facts of weekly
Page 50 and 51: 18 3 Linear Gaussian state space mo
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34 3 Linear Gaussian state space mo
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Chapter 4 Markov regime switching M
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4.1 Basic concepts 45 R t (%) 20 10
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4.1 Basic concepts 47 probability d
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4.3 Parameter estimation 49 X 1 X 2
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4.3 Parameter estimation 51 4.3.2.1
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4.4 Forecasting and decoding 53 4.4
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4.4 Forecasting and decoding 55 mod
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Chapter 5 Conditional heteroskedast
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5.1 Autoregressive conditional hete
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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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Applications of state space models in finance

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