Applications of state space models in finance

xxiv Used abbreviations and symbols
Q β
t
block matrix determining the nature of regression coefficients
Qsq Box-Ljung test statistic based on squared (excess) returns
q row dimension of diffuse vector δ;
the order of an ARCH process
Rt
system matrix in state equation;
multivariate vector of excess returns
R0
selection matrix
˜R matrix of unconditional variances of standardized residuals
R0,t
excess log-return of the market proxy
excess log-return of sector i
Ri,t
R2 coefficient of determination
¯R 2 adjusted coefficient of determination
ri,t
log-return of sector i
rt
vector of weighted sum of future innovations
r f
t
risk-free interest rate
r column dimension of the system matrix Rt
S − t−1 , S+ t−1 measures of asymmetry in tests for asymmetric GARCH effects
St
Markov chain
S (t) history of the Markov chain St up to time t
s2 p.e.v. for models with time-varying regression coefficients
s2 ∗
ML estimator of σ2 ∗ depending on generalized recursive residuals
SIZt
size factor
sk skewness of a series
T t
system matrix in state equation
T number of dates included in the sample
T St
term structure factor
ut
smoothing error
V t
smoothed state variance matrix
vt
one-step ahead prediction error
v †
t
˜v
recursive residuals
†
t
v
generalized recursive residuals
+ t
˜v
least squares residuals
+ t
generalized least squares residuals
V GSt
value growth spread factor
wt
sum of forward probabilities;
weighting factor in the context of WLS
w dimension of ψ
sequence of observations
Xt
X (t) history of the sequence of observations Xt up to time t
X (−u) sequence of random variables Xt with Xu being excluded
x (−u) observations xt with xu being excluded
xt
realized observation at time t;
asset payoff at time t
Y t
set of observations up to time t