Applications of state space models in finance

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98 6 Time-varying market beta risk of pan-European sectors Table 6.6 — continued Sector Model σ 2 × 10 4 σ 2 η × 10 2 σ 2 ζ × 10 2 φ β¯ 2 log L BIC R JB Q(12) LM(6) Construction RW 1.56 0.06 2638.4 −5.87 0.74 200.45*** 21.75*** 58.17*** MR 1.20 11.34 0.36*** 0.94 2629.8 −5.83 0.84 354.47*** 29.36*** 32.31*** MMR 1.22 7.46 0.04 0.00 2659.5 −5.90 0.83 260.43*** 24.24*** 33.40*** GWR 0.02 0.04 4693.4 −10.45 0.75 11.52*** 28.33*** 7.73 Financials RW 1.26 0.16 2721.2 −6.05 0.82 696.12*** 16.87* 37.17*** MR 0.88 9.98 0.20*** 0.94 2756.7 −6.12 0.90 1175.70*** 32.93*** 2.70 MMR 0.88 9.73 0.00 0.16** 2757.9 −6.12 0.90 1190.30*** 32.55*** 2.80 GWR 0.02 0.04 4657.2 −10.37 0.79 76.45*** 18.01** 12.36* Food RW 1.68 0.20 2593.0 −5.77 0.64 3049.40*** 22.14*** 95.44*** MR 1.67 0.23 0.99** 0.68 2593.7 −5.75 0.64 3121.40*** 22.07*** 94.78*** MMR 1.35 7.91 0.12 0.00 2609.3 −5.79 0.75 4750.80*** 19.23*** 69.40*** GWR 0.02 0.05 4669.3 −10.40 0.74 145.55*** 8.14* 5.90 Healthcare RW 2.84 0.18 2364.9 −5.26 0.57 184.90*** 12.15 43.46*** MR 2.82 0.31 0.98*** 0.81 2366.2 −5.25 0.57 195.24*** 12.71* 42.82*** MMR 2.56 6.31 0.13 0.00 2370.7 −5.26 0.64 298.90*** 12.86* 29.77*** GWR 0.02 0.09 4663.0 −10.38 0.59 74.59*** 11.97 2.67 Industrials RW 0.98 0.06 2843.1 −6.32 0.84 923.81*** 22.72*** 59.00*** MR 0.59 11.04 0.00 1.00 2881.8 −6.40 0.93 862.32*** 22.16*** 12.08* MMR 0.59 9.49 0.04 0.00 2888.0 −6.41 0.93 881.82*** 26.64*** 15.03** GWR 0.02 0.02 4675.5 −10.41 0.85 54.04*** 26.17*** 1.97 Insurance RW 1.83 0.30 2548.5 −5.67 0.84 215.62*** 20.19** 42.17*** MR 1.26 13.67 0.63*** 1.15 2570.5 −5.70 0.92 716.45*** 15.38** 8.05 MMR 1.25 11.80 0.16 0.04 2600.7 −5.77 0.91 550.26*** 17.39** 8.89 GWR 0.02 0.15 4699.6 −10.46 0.80 14.01*** 26.69*** 4.02 Media RW 3.00 0.51 2326.5 −5.17 0.75 2047.20*** 37.53*** 78.38*** MR 1.92 37.69 0.26*** 1.18 2338.5 −5.18 0.89 1185.30*** 22.59*** 7.92 MMR 2.00 25.25 0.22 0.00 2363.2 −5.24 0.87 1271.90*** 25.13*** 10.04 GWR 0.02 0.17 4660.8 −10.38 0.72 84.28*** 21.59** 3.67 Continued on the next page. . .
6.2 Modeling conditional betas 99 Table 6.6 — continued Sector Model σ 2 × 10 4 σ 2 η × 10 2 σ 2 ζ × 10 2 φ β¯ 2 log L BIC R JB Q(12) LM(6) Oil & Gas RW 3.78 0.14 2242.6 −4.99 0.48 314.84*** 26.11*** 101.05*** MR 3.24 12.76 0.44*** 0.75 2249.5 −4.99 0.61 794.60*** 22.84*** 56.55*** MMR 3.24 11.63 0.05 0.35*** 2252.0 −4.99 0.60 802.55*** 22.17*** 56.92*** GWR 0.02 0.09 4648.9 −10.35 0.52 10.94*** 13.06 0.99 Personal RW 1.53 0.08 2012.1 −5.87 0.77 758.40*** 26.17*** 100.02*** MR 1.52 0.13 0.98** 0.95 2012.5 −5.85 0.78 732.66*** 26.14*** 101.70*** MMR 1.36 3.52 0.07 0.04 2016.4 −5.87 0.82 427.06*** 19.92*** 90.20*** GWR 0.02 0.04 3540.5 −10.35 0.78 54.93*** 17.48** 23.13*** Retail RW 2.98 0.78 1765.7 −5.15 0.68 85.79*** 20.45** 15.24** MR 2.40 16.47 0.33** 0.90 1782.3 −5.18 0.78 72.60*** 14.63** 3.08 MMR 2.39 15.28 0.11 0.04 1785.2 −5.19 0.78 81.97*** 15.98** 2.78 GWR 0.02 0.13 3561.9 −10.41 0.63 71.40*** 16.73* 4.78 Technology RW 4.43 2.04 2128.8 −4.73 0.77 1426.00*** 22.32*** 46.33*** MR 4.14 6.24 0.92*** 1.48 2137.5 −4.74 0.79 1653.00*** 22.24*** 39.01*** MMR 3.36 31.22 0.35 0.04 2162.2 −4.79 0.85 2917.00*** 25.84*** 21.99*** GWR 0.02 0.26 4676.0 −10.41 0.74 69.99*** 8.42 1.97 Telecom RW 3.51 0.52 2258.2 −5.02 0.71 167.57*** 19.67** 54.57*** MR 3.40 1.55 0.95*** 1.25 2262.6 −5.01 0.73 167.95*** 21.36*** 49.59*** MMR 2.92 14.93 0.20 0.03 2274.9 −5.04 0.79 393.25*** 18.00** 24.05*** GWR 0.02 0.14 4662.5 −10.38 0.67 50.42*** 5.39 9.96 Travel RW 1.80 0.05 1960.8 −5.72 0.68 441.48*** 16.13* 55.50*** MR 1.36 10.91 0.04 0.75 1971.9 −5.74 0.80 416.05*** 11.88 22.53*** MMR 1.33 9.39 0.03 0.01 1982.3 −5.77 0.81 397.43*** 13.07* 23.61*** GWR 0.02 0.04 3537.5 −10.34 0.66 440.77*** 24.13*** 6.16 Utilities RW 1.38 0.14 2682.9 −5.97 0.68 74.91*** 20.21** 15.59** MR 1.35 0.37 0.97*** 0.74 2685.5 −5.96 0.69 95.78*** 21.89*** 14.21** MMR 1.23 3.57 0.07 0.00 2691.4 −5.97 0.73 171.70*** 23.10*** 10.42 GWR 0.02 0.07 4655.2 −10.36 0.66 35.79*** 17.48** 4.48
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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
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
Page 91 and 92: 5.1 Autoregressive conditional hete
Page 97 and 98: 5.2 Stochastic volatility 65 or the
Page 99 and 100: 5.2 Stochastic volatility 67 5.2.1.
Page 101 and 102: 5.2 Stochastic volatility 69 likeli
Page 103 and 104: 5.2 Stochastic volatility 71 linear
Page 105 and 106: 5.2 Stochastic volatility 73 3. An
Page 107 and 108: 5.3 Multivariate conditional hetero
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Page 116 and 117: 84 6 Time-varying market beta risk
Page 155 and 156: Chapter 7 A Kalman filter based con
Page 157 and 158: 7.1 Factor modeling 125 uncondition
Page 159 and 160: 7.1 Factor modeling 127 predictabil
Page 161 and 162: 7.1 Factor modeling 129 usefulness,
Page 163 and 164: 7.2 Specification of a conditional
Page 165 and 166: 7.3 The risk factors 133 Table 7.1:
Page 167 and 168: 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
Page 177 and 178: 7.4 Empirical results 145 β TS 0.4
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7.4 Empirical results 149 Table 7.8
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7.4 Empirical results 151 Table 7.9
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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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