paleoTS (version 0.6.2)

Kfiltertv: Time-varying Kalman filter calculations

Description

Time-varying Kalman filter calculations

Usage

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

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

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

Author

John Fricks ([e-mail])

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.

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)