Applications of state space models in finance

More documents

Recommendations

Info

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
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 16 and 17: xiv List of figures 6.14 Histograms
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 44 and 45: 12 2 Some stylized facts of weekly
Page 50 and 51: 18 3 Linear Gaussian state space mo
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
Page 89 and 90: Chapter 5 Conditional heteroskedast
Page 91 and 92: 5.1 Autoregressive conditional hete
Page 93 and 94:
5.1 Autoregressive conditional hete
Page 95 and 96:
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
Page 109 and 110:
Page 111 and 112:
Page 113:
Page 116 and 117:
84 6 Time-varying market beta risk
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
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 175 and 176:
Page 177 and 178:
7.4 Empirical results 145 β TS 0.4
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
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 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
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
Page 215 and 216:
Tables 183 Table C.5: Out-of-sample
Page 217 and 218:
Tables 185 Table C.7: Parameter est
Page 219 and 220:
Tables 187 Table C.7 — continued
Page 221 and 222:
Tables 189 Table C.8: Out-of-sample
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
show all

Applications of state space models in finance

Create successful ePaper yourself

Delete template?

Save as template?