Applications of state space models in finance

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188 Appendix C Table C.7 — continued Sector Model β1 β2 β3 β4 β5 β6 ¯R 2 Technology RLS 1.33*** −1.52*** 0.85*** 0.03*** 0.04* −0.73 0.66 RR5 1.02;1.54 −2.04;−0.01 0.32;1.35 −0.02;0.12 −0.05;0.10 −1.08;−0.38 0.65;0.82 (0.00;0.00) (0.00;0.91) (0.00;0.00) (0.00;0.98) (0.01;0.99) (0.00;0.00) RR1 0.83;2.08 −3.91;0.42 −0.29;1.61 −0.05;0.49 −0.16;0.30 −1.90;−0.10 0.54;0.92 (0.00;0.00) (0.00;0.98) (0.00;0.94) (0.00;1.00) (0.00;1.00) (0.00;0.56) Telecom RLS 0.99*** −1.09*** 1.10*** 0.03*** −0.01 −0.49 0.70 RR5 0.89;1.29 −1.48;−0.12 0.56;1.31 0.00;0.06 −0.06;0.01 −0.65;−0.40 0.62;0.82 (0.00;0.00) (0.00;0.38) (0.00;0.00) (0.00;0.99) (0.01;1.00) (0.00;0.00) RR1 0.65;1.68 −1.95;0.42 0.22;1.90 −0.03;0.20 −0.11;0.10 −0.92;−0.06 0.53;0.90 (0.00;0.00) (0.00;0.98) (0.00;0.22) (0.00;0.99) (0.04;1.00) (0.00;0.69) Travel RLS 1.04*** 0.18*** 0.63*** 0.02*** −0.03* −0.58 0.58 RR5 0.89;1.11 −0.22;0.32 0.13;0.93 −0.01;0.06 −0.07;0.02 −0.85;−0.35 0.47;0.65 (0.00;0.00) (0.00;1.00) (0.00;0.35) (0.00;0.89) (0.06;1.00) (0.00;0.00) RR1 0.59;1.38 −0.39;1.11 −0.56;1.20 −0.09;0.21 −0.12;0.12 −1.48;−0.08 0.29;0.88 (0.00;0.02) (0.00;1.00) (0.00;0.95) (0.00;1.00) (0.03;1.00) (0.00;0.68) Utilities RLS 0.64*** −0.10** 0.68*** 0.01 −0.02* −0.30 0.56 RR5 0.50;0.89 −0.34;0.06 0.42;0.75 −0.01;0.02 −0.08;0.01 −0.46;−0.24 0.50;0.65 (0.00;0.00) (0.00;1.00) (0.00;0.00) (0.00;1.00) (0.01;0.99) (0.00;0.00) RR1 0.25;1.12 −0.75;0.75 −0.28;1.20 −0.09;0.08 −0.13;0.08 −0.75;0.22 0.21;0.87 (0.00;0.04) (0.00;0.98) (0.00;1.00) (0.00;0.99) (0.01;0.99) (0.00;0.99)
Tables 189 Table C.8: Out-of-sample errors for multiple factor models. This table reports the estimated out-of-sample mean errors for the four multiple factor specifications. For each sector i, figures in parentheses denote the relative rank of a model’s mean absolute and squared error, respectively, where the model with the smallest error ranks first. Sector MAE (×10 2 ) MSE (×10 4 ) KF RLS RR5 RR1 KF RLS RR5 RR1 Automobiles 1.617 1.720 1.703 1.670 4.706 5.655 5.458 5.109 (1) (4) (3) (2) (1) (4) (3) (2) Banks 0.868 1.007 0.982 1.002 1.560 2.248 2.069 1.988 (1) (4) (2) (3) (1) (4) (3) (2) Basics 1.610 1.713 1.671 1.663 5.002 5.553 5.313 5.227 (1) (4) (3) (2) (1) (4) (3) (2) Chemicals 1.336 1.448 1.439 1.432 3.084 3.743 3.707 3.532 (1) (4) (3) (2) (1) (4) (3) (2) Construction 1.039 1.133 1.120 1.115 1.990 2.531 2.351 2.201 (1) (4) (3) (2) (1) (4) (3) (2) Financials 1.001 1.146 1.115 1.110 1.892 2.639 2.385 2.303 (1) (4) (3) (2) (1) (4) (3) (2) Food 1.162 1.249 1.247 1.206 2.731 3.089 3.053 2.872 (1) (4) (3) (2) (1) (4) (3) (2) Healthcare 1.283 1.357 1.368 1.348 3.181 3.547 3.538 3.488 (1) (3) (4) (2) (1) (4) (3) (2) Industrials 0.907 1.054 1.011 1.002 1.617 2.277 2.037 1.941 (1) (4) (3) (2) (1) (4) (3) (2) Insurance 1.280 1.509 1.466 1.392 3.279 5.460 4.878 4.183 (1) (4) (3) (2) (1) (4) (3) (2) Media 1.470 1.721 1.643 1.502 3.989 6.319 5.447 4.197 (1) (4) (3) (2) (1) (4) (3) (2) Oil & Gas 1.487 1.567 1.575 1.510 3.949 4.490 4.546 4.160 (1) (3) (4) (2) (1) (3) (4) (2) Personal 1.085 1.168 1.156 1.159 2.164 2.541 2.455 2.347 (1) (4) (2) (3) (1) (4) (3) (2) Retail 1.132 1.140 1.148 1.177 2.383 2.552 2.532 2.519 (1) (2) (3) (4) (1) (4) (3) (2) Technology 1.642 2.096 1.939 1.862 5.588 9.273 7.738 6.797 (1) (4) (3) (2) (1) (4) (3) (2) Telecom 1.424 1.551 1.469 1.445 3.789 4.589 4.059 3.949 (1) (4) (3) (2) (1) (4) (3) (2) Travel 1.443 1.495 1.476 1.499 3.798 4.238 4.071 4.172 (1) (3) (2) (4) (1) (4) (2) (3) Utilities 1.065 1.151 1.155 1.110 1.864 2.171 2.175 2.104 (1) (3) (4) (2) (1) (3) (4) (2) Average error 1.270 1.401 1.371 1.345 3.143 4.051 3.767 3.505 Average Rank 1.00 3.67 3.00 2.33 1.00 3.89 3.06 2.06
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Sascha Mergner Applications of Stat
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erschienen im Universitätsverlag G
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Bibliographische Information der De
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Contents List of figures . . . . .
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Contents ix 4.5 Model selection and
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Contents xi 7.5 Concluding remarks
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xiv List of figures 6.14 Histograms
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Notation and conventions The outlin
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xx Used abbreviations and symbols L
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xxii Used abbreviations and symbols
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xxiv Used abbreviations and symbols
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Preface The work on this book began
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Chapter 1 Introduction “Economist
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1.2 Research objectives 3 1.2 Resea
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1.3 Organization of the thesis 5 to
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8 2 Some stylized facts of weekly s
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10 2 Some stylized facts of weekly
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18 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
Page 169 and 170: 7.3 The risk factors 137 auxiliary
Page 171 and 172: 7.4 Empirical results 139 Table 7.4
Page 173 and 174: 7.4 Empirical results 141 are consi
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Page 185 and 186: 7.4 Empirical results 153 cumulativ
Page 187 and 188: Chapter 8 Conclusion and outlook Th
Page 189 and 190: Conclusion and outlook 157 cannot o
Page 191 and 192: Appendix A Brief review of asset pr
Page 193 and 194: A.3 Alternative asset pricing model
Page 195 and 196: Appendix B Figures
Page 197 and 198: Figures 165 β t β t β t 2.0 1.5
Page 209 and 210: Appendix C Tables
Page 211 and 212: Tables 179 Table C.1 — continued
Page 213 and 214: Tables 181 Table C.3: In-sample mea
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Page 217 and 218: Tables 185 Table C.7: Parameter est
Page 219: Tables 187 Table C.7 — continued
Page 223 and 224: References Abell, J. D. and T. M. K
Page 225 and 226: References 193 Bulla, J. (2006). Ap
Page 227 and 228: References 195 Fabozzi, F. J. and J
Page 229 and 230: References 197 Harvey, A. C., E. Ru
Page 231 and 232: References 199 Lie, F., R. Brooks,
Page 233 and 234: References 201 Shephard, N. (1993).
Page 235: State space models play a key role
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