| Title: | 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/6444.001.0001><http://econ.korea.ac.kr/~cjkim/>. |
| Authors: | Alex Hubbard [aut, cre] |
| Maintainer: | Alex Hubbard <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.3 |
| Built: | 2024-11-04 06:31:53 UTC |
| Source: | CRAN |
Check if list contains a name
contains(s, L)contains(s, L)
s |
a string name |
L |
a list object |
boolean
Generalized matrix inverse
gen_inv(m)gen_inv(m)
m |
matrix |
matrix inverse of m
Kim Filter
kim_filter(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)kim_filter(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)
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 |
list of cubes and matrices output by the Kim filter
## 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)## 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
kim_filter_cpp(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)kim_filter_cpp(ssm, yt, Xo = NULL, Xs = NULL, weight = NULL, smooth = FALSE)
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 |
list of cubes and matrices output by the Kim filter
R's implementation of the Moore-Penrose pseudo matrix inverse
Rginv(m)Rginv(m)
m |
matrix |
matrix inverse of m
Matrix self rowbind
self_rbind(mat, times)self_rbind(mat, times)
mat |
matrix |
times |
integer |
matrix
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
ss_prob(mat)ss_prob(mat)
mat |
square SxS matrix of probabilities with column sums of 1. S represents the number of states |
matrix of dimensions Sx1 with steady state probabilities
## Not run: library(kimfilter) Pm = rbind(c(0.8406, 0.0304), c(0.1594, 0.9696)) ss_prob(Pm) ## End(Not run)## 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
data(sw_dcf)data(sw_dcf)
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)
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/).