Applications of state space models in finance

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10 2 Some stylized facts of weekly sector return series Technology Media Telecom Oil Travel Utilities Food Healthcare Insurance Figure 2.1: Hierarchical cluster dendrogram for the set of excess sector returns. or clusters — of observations with similar characteristics. Hierarchical methods like the one employed here do not require the number of clusters to be predetermined. 2 From top to bottom three major clusters can be identified. The outer left cluster consists of the three sectors Technology, Media and Telecommunications (TMT). The chart suggests that the TMT cluster is isolated from the rest of the market. This reflects the sectors’ outstanding role during the dotcom bubble at the end of the 1990s. The center group of sectors ranges from Oil & Gas to Healthcare and represents the defensive end of the market. The remaining sectors constitute the cyclical part of the market. By moving the corresponding subtree one level further down, one can differentiate between financial and non-financial cyclicals. 2.2 Empirical properties Figure 2.2 displays the time series of original prices, of excess returns as defined by (2.2) and of squared excess returns for the overall market and the two sectors Insurance and Food & Beverage. An informal first look at these graphs suggests that the original sector series in levels are trending. Formally, the existence of a unit root can be confirmed by an augmented Dickey-Fuller test or the Phillips-Perron test. As the existence of unit roots in financial price series is extensively discussed in the empirical literature, the corresponding results are not reported here; for a detailed outline of unit root tests, see, for example, Pagan (1996). In the following, only excess returns will be considered. 2 The dendrogram has been generated using the hclust() function of the open-source statistical software package R 2.1.1 (R Development Core Team 2005) which can be downloaded from www.r-project.org. For an introductory outline of cluster analysis and its implementation, see, for example, Struyf et al. (1996) and Kaufman and Rousseeuw (2005). Banks Financials Automobiles Retail Basics Chemicals Personal Construction Industrials
2.2 Empirical properties 11 p t R t (%) 100 * R t (%) * R t (%) 600 500 400 300 200 100 20 10 0 −10 −20 200 150 100 50 0 (a) Broad 1990 1995 2000 2005 1990 1995 2000 2005 1990 1995 2000 2005 p t R t (%) 100 * R t (%) * R t (%) 600 500 400 300 200 100 20 10 0 −10 −20 500 400 300 200 100 0 (b) Insurance 1990 1995 2000 2005 1990 1995 2000 2005 1990 1995 2000 2005 p t R t (%) 100 * R t (%) * R t (%) 600 500 400 300 200 100 20 10 0 −10 −20 200 150 100 50 0 (c) Food & Beverages 1990 1995 2000 2005 1990 1995 2000 2005 1990 1995 2000 2005 Figure 2.2: Summaries of the weekly returns on the (i) broad market, (ii) the Insurance sector and (iii) Food & Beverages. Summaries from top to bottom are time series of original prices, excess returns and squared excess returns. Another obvious property illustrated by the returns and squared return series is that weeks of large absolute movements are followed by weeks with the same characteristics. This phenomenon, commonly referred to as volatility clustering, can be particularly observed in the second half of the sample, which includes the Asian crisis (1997), the Russian debt crisis (1998) and the boom and bust of the dotcom bubble (1998–2003). Univariate descriptive statistics for the data and some standard test statistics, which are referred to in the following subsections, are provided in Table 2.2. It can be seen that over the entire sample, the highest average weekly excess returns are offered by Healthcare (0.17%), Oil & Gas (0.15%) and Utilities (0.15%). The lowest are realized for Automobiles & Parts (0.02%), Insurance (0.04%) and Retail (0.06%). The risk, as measured by the annualized standard deviation, ranges from 14.64% for the defensive Utilities to 30.45% for the high risk sector Technology. 2.2.1 Thick tails The observed degree of kurtosis (ku) of market and sector returns reported in Table 2.2 generally exceeds the normal value of three. Compared to a normal distribution, the peaks are higher and the tails are heavier, which reflects that large outlying observations occur more often than can be expected under the assumption of normality. According
Page 1: Sascha Mergner Applications of Stat
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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 16 and 17: xiv List of figures 6.14 Histograms
Page 19: Notation and conventions The outlin
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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
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Page 75 and 76: Chapter 4 Markov regime switching M
Page 77 and 78: 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
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5.1 Autoregressive conditional hete
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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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