Applications of state space models in finance

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190 Appendix C Table C.9: Fama-MacBeth regression results II. This table presents the estimation results for the Fama-MacBeth regressions with the regressors being the out-of-sample loadings on the BMR, V GS, SIZ and T S factors only. The factor loadings have been estimated from one of the time series regressions of excess sector returns on the set of explanatory variables as presented in 7.4.1. Average coefficients are expressed as percent per week ×10. The number of cross-sectional regressions is 520 for each model. t-statistics are reported in parentheses with the relevant critical value at the 95% (90%, 99%) level being −1.96 (−1.65, −2.59). Significant average coefficients are printed in bold numbers. The last column reports average adjusted coefficients of determination. Model BMR V GS SIZ T S ¯ R 2 A. 22 February 1995–2 February 2005 KF 1.128 0.532 0.346 −13.225 0.229 (1.073) (0.650) (0.463) (−1.895) RLS 0.841 0.546 1.145 11.757 0.216 (0.681) (0.381) (1.130) (0.315) RR5 0.717 0.680 1.329 14.079 0.213 (0.585) (0.555) (1.400) (0.688) RR1 0.312 0.647 0.316 −7.041 0.218 (0.291) (0.780) (0.416) (−0.827) B. 22 February 1995–8 March 2000 KF 2.155 −1.375 1.856 −23.141 0.140 (1.637) (−1.132) (1.690) (−2.262) RLS 1.518 −3.263 3.549 26.942 0.116 (1.123) (−1.450) (2.605) (0.587) RR5 1.071 −2.175 3.853 33.279 0.130 (0.788) (−1.104) (2.905) (0.942) RR1 1.408 −1.498 2.031 −18.327 0.127 (1.043) (−1.264) (1.820) (−1.461) C. 15 March 2000–12 March 2003 KF −2.727 3.362 −2.466 −5.080 0.371 (−1.159) (1.973) (−1.708) (−0.353) RLS −3.974 6.663 −2.134 26.108 0.377 (−1.359) (2.443) (−0.956) (0.296) RR5 −3.363 5.329 −2.130 0.556 0.362 (−1.113) (2.370) (−1.058) (0.019) RR1 −3.081 3.908 −2.729 −2.148 0.362 (−1.295) (2.155) (−1.855) (−0.128) D. 19 March 2003–2 February 2005 KF 4.505 1.128 0.780 0.301 0.241 (2.243) (1.564) (0.652) (0.035) RLS 6.670 1.001 −0.068 −51.495 0.228 (2.523) (1.033) (−0.044) (−0.815) RR5 6.246 0.918 0.087 −15.673 0.199 (2.778) (1.211) (0.064) (−0.669) RR1 2.774 1.194 0.569 15.294 0.231 (1.327) (1.784) (0.472) (1.180)
References Abell, J. D. and T. M. Krueger (1989). Macroeconomic influences on beta. Journal of Economics and Business 41 (2), 185–193. Aguilar, O. and M. West (2000). Bayesian dynamic factor models and portfolio allocation. Journal of Business and Economic Statistics 18 (3), 338–357. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. Petrov and F. Csake (Eds.), Proceedings of the Second International Symposium on Information Theory, Akademiai Kiado, Budapest, Hungary. Alexander, C. (2000). Orthogonal methods for generating large positive semi-definite covariance matrices. ISMA Centre Discussion Papers in Finance 2000-06, ISMA Centre, University of Reading, UK. Available at http://www.ismacentre.rdg.ac.uk (9.5.2006). Alexander, C. (2001). Market Models. A Guide to Financial Data Analysis. West Sussex, UK: John Wiley & Sons. Andersen, T. and B. Sorensen (1996). GMM estimation of a stochastic volatility model: A Monte Carlo study. Journal of Business and Economic Statistics 14 (3), 392–452. Andersen, T. G. and T. Bollerslev (1998). ARCH and GARCH models. In S. Kotz, C. B. Read, and D. L. Banks (Eds.), Encyclopedia of Statistical Sciences, Volume II, Chapter 49, pp. 6–16. New York, NY, USA: John Wiley & Sons. Andersen, T. G., T. Bollerslev, P. F. Christoffersen, and F. X. Diebold (2005). Volatility forecasting. Working Paper 11188, National Bureau of Economic Research, Cambridge, MA, USA. Available at http://www.nber.org/papers/w11188 (6.4.2005). Andersen, T. G., T. Bollerslev, and F. X. Diebold (2002). Parametric and nonparametric volatility measurement. NBER Technical Working Paper 0279, National Bureau of Economic Research, Inc. Available at http://ideas.repec.org/p/nbr/nberte/0279.html (6.2.2006). Andersen, T. G., T. Bollerslev, F. X. Diebold, and J. Wu (2005). A framework for exploring the macroeconomic determinants of systematic risk. American Economic Review Papers and Proceedings. Available at http://www.aeaweb.org/ annual mtg papers/2005/0107 1015 0101.pdf (17.1.2005). Anderson, B. D. O. and J. B. Moore (1979). Optimal Filtering. Englewood Cliffs, NJ, USA: Prentice Hall. Ansley, C. F. and R. Kohn (1985). Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions. Annals of Statistics 13 (4), 1286–1316. Asai, M., M. McAleer, and J. Yu (2006). Multivariate stochastic volatility: A review. Econometric Reviews 25 (2–3), 145–175. Baillie, R. T. and T. Bollerslev (1990). A multivariate generalized ARCH approach to modeling risk premia in forward foreign exchange rate markets. Journal of International Money and Finance 9 (3), 309–324. Banz, R. W. (1981). The relationship between return and the market value of common stocks. Journal of Financial Economics 9 (1), 3–18. Basu, S. (1977). Investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis. Journal of Finance 32 (3), 663–682.
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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
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7.3 The risk factors 137 auxiliary
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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
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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
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Page 233 and 234: References 201 Shephard, N. (1993).
Page 235: State space models play a key role
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