astsa (version 1.10)

Ksmooth0: Kalman Filter and Smoother - Time invariant model without inputs

Description

Returns both the filtered values and smoothed values for the state-space model.

Usage

Ksmooth0(num, y, A, mu0, Sigma0, Phi, cQ, cR)

Arguments

num

number of observations

y

data matrix, vector or time series

A

time-invariant observation matrix

mu0

initial state mean vector

Sigma0

initial state covariance matrix

Phi

state transition matrix

cQ

Cholesky-type decomposition of state error covariance matrix Q -- see details below

cR

Cholesky-type decomposition of observation error covariance matrix R -- see details below

Value

xs

state smoothers

Ps

smoother mean square error

x0n

initial mean smoother

P0n

initial smoother covariance

J0

initial value of the J matrix

J

the J matrices

xp

one-step-ahead prediction of the state

Pp

mean square prediction error

xf

filter value of the state

Pf

mean square filter error

like

the negative of the log likelihood

Kn

last value of the gain

%% ~Describe the value returned %% If it is a LIST, use %% \item{comp1 }{Description of 'comp1'} %% \item{comp2 }{Description of 'comp2'} %% ...

Details

Practically, the script only requires that Q or R may be reconstructed as t(cQ)%*%(cQ) or t(cR)%*%(cR), respectively, which allows more flexibility.

References

http://www.stat.pitt.edu/stoffer/tsa4/

See also http://www.stat.pitt.edu/stoffer/tsa4/chap6.htm for an explanation of the difference between levels 0, 1, and 2.