SS {sspir} | R Documentation |
Creates an SS-object describing a Gaussian state space model.
SS(y = NA, x = NA, Fmat = function(tt, x, phi) { NA }, Gmat = function(tt, x, phi) { NA }, Vmat = function(tt, x, phi) { NA }, Wmat = function(tt, x, phi) { NA }, m0 = 0, C0 = NA, phi = NA)
y |
a matrix giving a multivariate time series of
observations. The observation at time tt is
y[,tt] . The dimension of y is d times n. |
x |
a list of entities (eg. covariates) passed as argument to the functions
Fmat , Gmat , Vmat , and Wmat . |
Fmat |
a function depending on the parameter-vector phi ,
covariates x and returns the p times d design matrix at time
tt . |
Gmat |
a function depending on the parameter-vector phi ,
covariates x and returns the p times p evolution matrix at
time tt . |
Vmat |
a function depending on the parameter-vector phi ,
covariates x and returns the d times d (positive definit)
variance matrix at time tt . |
Wmat |
a function depending on the parameter-vector phi ,
covariates x and returns the p times p (positive
semidefinite) evolution variance matrix at time tt . |
m0 |
a p times 1 matrix giving the initial state. |
C0 |
a p times p variance matrix giving the variance matrix of the initial state. |
phi |
a parameter vector passed as argument to the functions Fmat , Gmat , Vmat , and Wmat . |
The state space model is given by
Y_t = F_t^T * theta_t + v_t, v_t ~ N(0,V_t)
theta_t = G_t * theta_{t-1} + w_t, w_t ~ N(0,W_t)
for t=1,...,n. The matrices F_t, G_t, V_t, and W_t may depend on a parameter vector phi. The initialization is given as
theta_0 ~ N(m_0,C_0).
An object of class SS
, which is a list with the following components
y |
as input. |
x |
as input. |
Fmat |
as input. |
Gmat |
as input. |
Vmat |
as input. |
Wmat |
as input. |
m0 |
as input. |
C0 |
as input. |
phi |
as input. |
n |
the number of time points |
d |
the dimension of each observation. |
p |
the dimension of the state vector at each timepoint. |
ytilde |
for use in the extended Kalman filter. |
iteration |
for use in the extended Kalman filter. |
m |
after Kalman filtering (or smoothing), holds the conditional mean of the state vectors given the observations up til time t (filtering) or all observations (smoothing). This is organised in a p times n dimensional matrix holding m_t (m_t^*) in columns. |
C |
after Kalman filtering (or smoothing), holds the conditional variance of the state vectors given the observations up til time t (filtering) or all observations (smoothing). This is organised in a list holding the p times p dimensional matrices C_t (C_t^*). |
mu |
after Kalman smoothing, holds the conditional mean of the signal (μ_t=F_t^top theta_t) given all observations. This is organised in a d times n dimensional matrix holding μ_t in columns. |
likelihood |
the log-likelihood value after Kalman filtering. |
Claus Dethlefsen and Søren Lundbye-Christensen
ssm
for a glm-like interface of specifying
models, kfilter
for Kalman filter and
smoother
for Kalman smoother.
time <- 1:length(UKgas) gasmodel <- ssm( log10(UKgas) ~ -1+ tvar(polytime(time,1))+ tvar(sumseason(time,12)),time=time) gasmodel$ss$phi <- StructTS(log10(UKgas),type="BSM")$coef[c(4,1,2,3)] fit <- kfs(gasmodel) plot( ts( t(fit$m[1:3,]) ) )