Package 'kalmanfilter'

Kalman Filter

Description

Kalman Filter

Usage

kalman_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 matrix (or array of length yt), initial guess for the unobserved components P0 - N_b x N_b matrix (or array of length yt), initial guess for the covariance matrix of the unobserved components Dm - N_b x 1 matrix (or array of length yt), constant matrix for the state equation Am - N_y x 1 matrix (or array of length yt), constant matrix for the observation equation Fm - N_b X p matrix (or array of length yt), state transition matrix Hm - N_y x N_b matrix (or array of length yt), observation matrix Qm - N_b x N_b matrix (or array of length yt), state error covariance matrix Rm - N_y x N_y matrix (or array of length yt), state error covariance matrix betaO - N_y x N_o matrix (or array of length yt), coefficient matrix for the observation exogenous data betaS - N_b x N_s matrix (or array of length yt), coefficient matrix for the state exogenous data
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 Kalman filter

Examples

## Not run: 
#Stock and Watson Markov switching dynamic common factor
library(kalmanfilter)
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))
  
#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 = kalman_filter(ssm, yt, smooth = TRUE)

## End(Not run)

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Stock and Watson Dynamic Common Factor Data Set

Description

Stock and Watson 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/>.

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Treasuries

Description

Treasuries

Usage

data(treasuries)

Format

data.table with columns DATE, VARIABLE, VALUE, and MATURITY The data is quarterly frequency with variables DGS1MO, DGS3MO, DGS6MO, DGS1, DGS2, DGS3, DGS5, DGS7, DGS10, DGS20, and DGS30

Source

FRED

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