| Type: | Package |
| Title: | Kim Filter |
| Version: | 1.0.3 |
| Date: | 2024-03-01 |
| Description: | 'Rcpp' implementation of the multivariate Kim filter, which combines the Kalman and Hamilton filters for state probability inference. The filter is designed for state space models and can handle missing values and exogenous data in the observation and state equations. Kim, Chang-Jin and Charles R. Nelson (1999) "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications" <doi:10.7551/mitpress/6444.001.0001>http://econ.korea.ac.kr/~cjkim/. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | Rcpp (≥ 1.0.9) |
| LinkingTo: | Rcpp, RcppArmadillo |
| RoxygenNote: | 7.2.3 |
| Suggests: | data.table (≥ 1.14.2), maxLik (≥ 1.5-2), ggplot2 (≥ 3.3.6), gridExtra (≥ 2.3), knitr, rmarkdown, testthat |
| VignetteBuilder: | knitr |
| Encoding: | UTF-8 |
| NeedsCompilation: | yes |
| Packaged: | 2024-03-08 03:43:30 UTC; alex.hubbard |
| Author: | Alex Hubbard [aut, cre] |
| Maintainer: | Alex Hubbard <hubbard.alex@gmail.com> |
| Depends: | R (≥ 3.5.0) |
| Repository: | CRAN |
| Date/Publication: | 2024-03-08 05:10:02 UTC |
kimfilter: Kim Filter
Description
'Rcpp' implementation of the multivariate Kim filter, which combines the Kalman and Hamilton filters for state probability inference. The filter is designed for state space models and can handle missing values and exogenous data in the observation and state equations. Kim, Chang-Jin and Charles R. Nelson (1999) "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications" doi:10.7551/mitpress/6444.001.0001http://econ.korea.ac.kr/~cjkim/.
Author(s)
Maintainer: Alex Hubbard hubbard.alex@gmail.com
R's implementation of the Moore-Penrose pseudo matrix inverse
Description
R's implementation of the Moore-Penrose pseudo matrix inverse
Usage
Rginv(m)
Arguments
m |
matrix |
Value
matrix inverse of m
Check if list contains a name
Description
Check if list contains a name
Usage
contains(s, L)
Arguments
s |
a string name |
L |
a list object |
Value
boolean
Generalized matrix inverse
Description
Generalized matrix inverse
Usage
gen_inv(m)
Arguments
m |
matrix |
Value
matrix inverse of m
Kim Filter
Description
Kim Filter
Usage
kim_filter(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)
Arguments
ssm |
list describing the state space model, must include names B0 - N_b x 1 x n_state array of matrices, initial guess for the unobserved components P0 - N_b x N_b x n_state array of matrices, initial guess for the covariance matrix of the unobserved components Dm - N_b x 1 x n_state array of matrices, constant matrix for the state equation Am - N_y x 1 x n_state array of matrices, constant matrix for the observation equation Fm - N_b X p x n_state array of matrices, state transition matrix Hm - N_y x N_b x n_state array of matrices, observation matrix Qm - N_b x N_b x n_state array of matrices, state error covariance matrix Rm - N_y x N_y x n_state array of matrices, state error covariance matrix betaO - N_y x N_o x n_state array of matrices, coefficient matrix for the observation exogenous data betaS - N_b x N_s x n_state array of matrices, coefficient matrix for the state exogenous data Pm - n_state x n_state matrix, state transition probability matrix |
yt |
N x T matrix of data |
Xo |
N_o x T matrix of exogenous observation data |
Xs |
N_s x T matrix of exogenous state |
weight |
column matrix of weights, T x 1 |
smooth |
boolean indication whether to run the backwards smoother |
Value
list of cubes and matrices output by the Kim filter
Examples
## Not run:
#Stock and Watson Markov switching dynamic common factor
library(kimfilter)
library(data.table)
data(sw_dcf)
data = sw_dcf[, colnames(sw_dcf) != "dcoinc", with = FALSE]
vars = colnames(data)[colnames(data) != "date"]
#Set up the state space model
ssm = list()
ssm[["Fm"]] = rbind(c(0.8760, -0.2171, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
c(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0.0364, -0.0008, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, -0.2965, -0.0657, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, -0.3959, -0.1903, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.2436, 0.1281),
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0))
ssm[["Fm"]] = array(ssm[["Fm"]], dim = c(dim(ssm[["Fm"]]), 2))
ssm[["Dm"]] = matrix(c(-1.5700, rep(0, 11)), nrow = nrow(ssm[["Fm"]]), ncol = 1)
ssm[["Dm"]] = array(ssm[["Dm"]], dim = c(dim(ssm[["Dm"]]), 2))
ssm[["Dm"]][1,, 2] = 0.2802
ssm[["Qm"]] = diag(c(1, 0, 0, 0, 0.0001, 0, 0.0001, 0, 0.0001, 0, 0.0001, 0))
ssm[["Qm"]] = array(ssm[["Qm"]], dim = c(dim(ssm[["Qm"]]), 2))
ssm[["Hm"]] = rbind(c(0.0058, -0.0033, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0),
c(0.0011, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0),
c(0.0051, -0.0033, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0),
c(0.0012, -0.0005, 0.0001, 0.0002, 0, 0, 0, 0, 0, 0, 1, 0))
ssm[["Hm"]] = array(ssm[["Hm"]], dim = c(dim(ssm[["Hm"]]), 2))
ssm[["Am"]] = matrix(0, nrow = nrow(ssm[["Hm"]]), ncol = 1)
ssm[["Am"]] = array(ssm[["Am"]], dim = c(dim(ssm[["Am"]]), 2))
ssm[["Rm"]] = matrix(0, nrow = nrow(ssm[["Am"]]), ncol = nrow(ssm[["Am"]]))
ssm[["Rm"]] = array(ssm[["Rm"]], dim = c(dim(ssm[["Rm"]]), 2))
ssm[["B0"]] = matrix(c(rep(-4.60278, 4), 0, 0, 0, 0, 0, 0, 0, 0))
ssm[["B0"]] = array(ssm[["B0"]], dim = c(dim(ssm[["B0"]]), 2))
ssm[["B0"]][1:4,, 2] = rep(0.82146, 4)
ssm[["P0"]] = rbind(c(2.1775, 1.5672, 0.9002, 0.4483, 0, 0, 0, 0, 0, 0, 0, 0),
c(1.5672, 2.1775, 1.5672, 0.9002, 0, 0, 0, 0, 0, 0, 0, 0),
c(0.9002, 1.5672, 2.1775, 1.5672, 0, 0, 0, 0, 0, 0, 0, 0),
c(0.4483, 0.9002, 1.5672, 2.1775, 0, 0, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0.0001, 0, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0.0001, 0, 0, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, 0.0001, -0.0001, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, -0.0001, 0.0001, 0, 0, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, 0.0001, -0.0001, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, -0.0001, 0.0001, 0, 0),
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0001, -0.0001),
c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.0001, 0.0001))
ssm[["P0"]] = array(ssm[["P0"]], dim = c(dim(ssm[["P0"]]), 2))
ssm[["Pm"]] = rbind(c(0.8406, 0.0304),
c(0.1594, 0.9696))
#Log, difference and standardize the data
data[, c(vars) := lapply(.SD, log), .SDcols = c(vars)]
data[, c(vars) := lapply(.SD, function(x){
x - shift(x, type = "lag", n = 1)
}), .SDcols = c(vars)]
data[, c(vars) := lapply(.SD, scale), .SDcols = c(vars)]
#Convert the data to an NxT matrix
yt = t(data[, c(vars), with = FALSE])
kf = kim_filter(ssm, yt, smooth = TRUE)
## End(Not run)
Kim Filter
Description
Kim Filter
Usage
kim_filter_cpp(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)
Arguments
ssm |
list describing the state space model, must include names B0 - N_b x 1 x n_state array of matrices, initial guess for the unobserved components P0 - N_b x N_b x n_state array of matrices, initial guess for the covariance matrix of the unobserved components Dm - N_b x 1 x n_state array of matrices, constant matrix for the state equation Am - N_y x 1 x n_state array of matrices, constant matrix for the observation equation Fm - N_b X p x n_state array of matrices, state transition matrix Hm - N_y x N_b x n_state array of matrices, observation matrix Qm - N_b x N_b x n_state array of matrices, state error covariance matrix Rm - N_y x N_y x n_state array of matrices, state error covariance matrix betaO - N_y x N_o x n_state array of matrices, coefficient matrix for the observation exogenous data betaS - N_b x N_s x n_state array of matrices, coefficient matrix for the state exogenous data Pm - n_state x n_state matrix, state transition probability matrix |
yt |
N x T matrix of data |
Xo |
N_o x T matrix of exogenous observation data |
Xs |
N_s x T matrix of exogenous state |
weight |
column matrix of weights, T x 1 |
smooth |
boolean indication whether to run the backwards smoother |
Value
list of cubes and matrices output by the Kim filter
Matrix self rowbind
Description
Matrix self rowbind
Usage
self_rbind(mat, times)
Arguments
mat |
matrix |
times |
integer |
Value
matrix
Steady State Probabilities
Description
Finds the steady state probabilities from a transition matrix mat = |p_11 p_21 ... p_m1| |p_12 p_22 ... p_m2| |... ...| |p_1m p_2m ... p_mm| where the columns sum to 1
Usage
ss_prob(mat)
Arguments
mat |
square SxS matrix of probabilities with column sums of 1. S represents the number of states |
Value
matrix of dimensions Sx1 with steady state probabilities
Examples
## Not run:
library(kimfilter)
Pm = rbind(c(0.8406, 0.0304),
c(0.1594, 0.9696))
ss_prob(Pm)
## End(Not run)
Stock and Watson Markov Switching Dynamic Common Factor Data Set
Description
Stock and Watson Markov Switching Dynamic Common Factor Data Set
Usage
data(sw_dcf)
Format
data.table with columns DATE, VARIABLE, VALUE, and MATURITY The data is monthly frequency with variables ip (industrial production), gmyxpg (total personal income less transfer payments in 1987 dollars), mtq (total manufacturing and trade sales in 1987 dollars), lpnag (employees on non-agricultural payrolls), and dcoinc (the coincident economic indicator)
Source
Kim, Chang-Jin and Charles R. Nelson (1999) "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications" <doi:10.7551/mitpress/6444.001.0001><http://econ.korea.ac.kr/~cjkim/> (http://econ.korea.ac.kr/~cjkim/).