astsa: Kfilter2 – R documentation

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Kfilter2

Kalman Filter - Model may be time varying or have inputs or correlated errors

Description

Returns the filtered values for the state space model. In addition, the script returns the evaluation of the likelihood at the given parameter values and the innovation sequence.

Usage

Kfilter2(num, y, A, mu0, Sigma0, Phi, Ups, Gam, Theta, cQ, cR, 
          S, input)

Arguments

`num`	number of observations
`y`	data matrix, vector or time series
`A`	time-varying observation matrix, an array with `dim = c(q,p,n)`
`mu0`	initial state mean
`Sigma0`	initial state covariance matrix
`Phi`	state transition matrix
`Ups`	state input matrix; use `Ups = 0` if not needed
`Gam`	observation input matrix; use `Gam = 0` if not needed
`Theta`	state error pre-matrix
`cQ`	Cholesky decomposition of state error covariance matrix Q – see details below
`cR`	Cholesky-type decomposition of observation error covariance matrix R – see details below
`S`	covariance-type matrix of state and observation errors
`input`	matrix or vector of inputs having the same row dimension as y; use `input = 0` if not needed

Value

`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
`innov`	innovation series
`sig`	innovation covariances
`K`	last value of the gain, needed for smoothing

Author(s)

D.S. Stoffer

References

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

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

astsa

Applied Statistical Time Series Analysis

v1.12

GPL-3

Authors

David Stoffer

Initial release

2020-12-20