Kfiltertv: Time-varying Kalman filter calculations

In paleoTS: Analyze Paleontological Time-Series

Time-varying Kalman filter calculations

Description

Time-varying Kalman filter calculations

Usage

Kfiltertv(num, y, Atv, mu0, Sigma0, Phitv, Ups, Gam, Qtv, Rtv, input)

Arguments

num	the number of samples in the time-series
y	values of the time-series
Atv	q x p x n observation array
mu0	p x 1 vector setting the mean of the system at time zero
Sigma0	p x p variance matrix of the system at time zero
Phitv	p x p x n array reflecting autoregression of the state variables
Ups	p x r matrix with the coefficients/parameters relating the inputs to the system equation
Gam	q x r matrix with the coefficients/parameters relating the inputs to the observation equation
Qtv	p x p x n array of system stochastic variance; user needs to ensure positive definite
Rtv	q x q x n array observation stochastic variance; user needs to ensure positive definite
input	n x r array of the exogenous variables/covariates

Details

For the dimensions of the argument arrays, n is the length of the time-series, q is the dimension of the observation variable(s), p is the dimension of the state variable(s), and r isthe dimension of the input variable(s).

This function is based on the Kfilter function of the astsa package, modified modified to allow for time-varying terms for the Kalman filter. This modification facilitates fitting a broader array of models and handling non-uniform temporal spacing of samples. See the documentation for that function, and the reference below for additional information.

Value

A list of the following elements:

• 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 log-likelihood

• innov innovation series

• sig innovation covariances

• Kn last value of the gain, needed for smoothing

Note

This function is used in the internal SSM log-likelihood functions for the models. The user will not need to use this they create their own model-fitting functions.

Author(s)

John Fricks ([e-mail])

References

Shumway, R. H., and D. S. Stoffer. 2017. Time Series Analysis and its Applications (4th Ed.) Springer International.

Examples

y <- sim.GRW(ms = 0, vs = 1, vp = 0)
n <- length(y)
kf <- Kfiltertv(n ,y = y$mm, Atv = array(1, dim = c(1,1,n)), mu0 = y$mm[1],
                Sigma0 = y$vv[1]/y$nn[1], Phitv = array(1, dim = c(1,1,n)),
                Ups = NULL, Gam = NULL, Qtv = array(1, dim = c(1,1,n)),
                Rtv = array(0, dim = c(1,1,n)), input = NULL)

paleoTS documentation built on Sept. 11, 2024, 9:18 p.m.