Applications of state space models in finance

List of figures
2.1 Hierarchical cluster dendrogram for the set of excess sector returns. . . . 10
2.2 Summaries of the weekly returns on the (i) broad market, (ii) the Insurance
sector and (iii) Food & Beverages. . . . . . . . . . . . . . . . . . . 11
2.3 Autocorrelation functions of the broad market, the Insurance sector and
Food & Beverages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 CUSUMSQ tests with 5% confidence intervals for the excess return series
of (a) Insurance and (b) Food & Beverages. . . . . . . . . . . . . . . . . 15
4.1 (a) Weekly percentage log-return series of the Technology sector and
(b) histogram with a fitted normal distribution. . . . . . . . . . . . . . . 45
4.2 Histogram of weekly log-returns of the Technology sector and fitted mixtures
with (a) two and (b) three normal distributions. . . . . . . . . . . 47
4.3 Basic structure of a hidden Markov model. . . . . . . . . . . . . . . . . 49
6.1 Conditional volatility estimates for the Telecommunications sector. . . . 95
6.2 Weekly excess log-return series of (a) Automobiles and (b) the broad
market. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 (a) Residuals from the auxiliary heteroskedastic regression model and
(b) GLS weighting factor for Automobiles and the overall market. . . . 104
6.4 Weighted weekly excess log-return series of (a) Automobiles and (b) the
broad market. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.5 Conditional random walk and generalized random walk beta estimates
for the Automobiles sector. . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.6 Boxplots of the conditional beta series for the Insurance sector. . . . . . 110
6.7 t-GARCH and stochastic volatility based betas for the Insurance sector. 111
6.8 Markov switching betas for the Insurance sector. . . . . . . . . . . . . . 111
6.9 Kalman filter betas for the Insurance sector. . . . . . . . . . . . . . . . . 112
6.10 In-sample forecasting evaluation: (a) average MAE and MSE across sectors
and (b) average ranks across sectors. . . . . . . . . . . . . . . . . . 114
6.11 Histograms of Spearman’s in-sample rank correlations. . . . . . . . . . . 115
6.12 Out-of-sample forecasting evaluation (100 samples): (a) average MAE
and MSE across sectors and (b) average ranks across sectors. . . . . . . 117
6.13 Histograms of Spearman’s out-of-sample rank correlations (100 samples). 118