| Library: | times |
| See also: | kfilter kem |
| Quantlet: | ksmoother | |
| Description: | Calculates a smoothed time serie (uni- or multivariate) using the Kalman smoother equations. The state-space model is assumed to be in the following form: y_t = H x_t + v_t x_t = F x_t-1 + w_t x_0 ~ (mu,Sig), v_t ~ (0,Q), w_t ~ (0,R) All parameters are assumed known. |
| Usage: | fy = ksmoother(y,mu,Sig,H,F,Q,R) | |
| Input: | ||
| y | T x m matrix of observed time series, T is the number of observations, m is the dimension of time series | |
| mu | n x 1 vector, the mean of the initial state | |
| Sig | n x n covariance matrix of the initial state | |
| H | m x n matrix | |
| F | n x n matrix | |
| Q | m x m variance-covariance matrix | |
| R | n x n variance-covariance matrix | |
| Output: | ||
| fy | T x p matrix of filtered time series | |
library("xplore")
library("times")
library("plot")
serie = read("kalman1.dat")
y = serie[,2]
mu = 10
Sig = 0
H = 1
F = 1
Q = 9
R = 9
sy = ksmoother(y,mu,Sig,H,F,Q,R)
sserie = serie[,1]~serie[,2]~sy
data = sserie[,1]~sserie[,2]
data = setmask(data, "line", "red", "thin")
sdata = sserie[,1]~sserie[,3]
sdata = setmask(sdata, "line", "blue", "thin")
disp = createdisplay(1,1)
show(disp,1,1, data, sdata)
setgopt(disp,1,1, "title", "Kalman smoother 1")
Original serie is displayed with red colour, filtered serie is displayed with blue colour. (y is a lagged random walk with errors.)
library("xplore")
library("times")
library("plot")
serie = read("kalman3.dat")
y = serie[,2:3]
mu = #(20,0)
Sig = #(0,0)~#(0,0)
H = #(0.3,-0.3)~#(1,1)
F = #(1,0)~#(1,0)
Q = #(9,0)~#(0,9)
R = #(0,0)~#(0,9)
sy = ksmoother(y,mu,Sig,H,F,Q,R)
sserie = serie[,1]~serie[,2]~serie[,3]~sy[,1]~sy[,2]
data1 = sserie[,1]~sserie[,2]
data1 = setmask(data1, "line", "red", "thin")
sdata1 = sserie[,1]~sserie[,4]
sdata1 = setmask(sdata1, "line", "blue", "thin")
data2 = sserie[,1]~sserie[,3]
data2 = setmask(data2, "line", "red", "thin")
sdata2 = sserie[,1]~sserie[,5]
sdata2 = setmask(fdata2, "line", "blue", "thin")
disp = createdisplay(2,1)
show(disp,1,1, data1, sdata1)
setgopt(disp, 1, 1, "title", "Kalman smoother 2 - 1st element")
show(disp,2,1, data2, sdata2)
setgopt(disp,2,1, "title", "Kalman smoother 2 - 2nd element")
Original serie is displayed with red colour, filtered serie is displayed with blue colour. (y is a lagged bivariate MA process with errors.)
library("xplore")
library("times")
library("plot")
serie = read("kalman2.dat")
y = serie[,2]
mu = #(0,0)
Sig = #(0,0)~#(0,0)
H = #(1,0)'
F = #(0.5,1)~#(-0.3,0)
R = #(1,0)~#(0,0)
Q = 4
fy = ksmoother(y,mu,Sig,H,F,Q,R)
sserie = serie[,1]~serie[,2]~sy
data1 = sserie[,1]~sserie[,2]
data1 = setmask(data1, "line", "red", "thin")
sdata1 = sserie[,1]~sserie[,3]
sdata1 = setmask(sdata1, "line", "blue", "thin")
disp = createdisplay(1,1)
show(disp,1,1, data1, sdata1)
setgopt(disp,1,1, "title", "Kalman smoother 3")
Original serie is displayed with red colour, filtered serie is displayed with blue colour. (y is an AR(2) process with errors.)