Library: | times |
See also: | kfilter ksmoother kem |
Quantlet: | kemitor | |
Description: | Calculates observations of a given state-space model. The state-space model is assumed to be in the following form: y_t = H x_t + ErrY_t x_t = F x_t-1 + ErrX_t x_0 = mu |
Usage: | y = kemitor(T,mu,H,F,ErrY,ErrX) | |
Input: | ||
T | number of observations to be generated | |
mu | n x 1 vector (starting point of the model) | |
H | m x n matrix | |
F | n x n matrix | |
ErrY | T x m matrix of errors | |
ErrX | T x n matrix of errors | |
Output: | ||
y | T x m matrix of generated time series, T is the number of generated observations, m is the dimension of generated time series |
library("xplore") library("plot") library("times") randomize(0) T = 100 mu = 10 H = 1 F = 1 ErrY = normal(T) .* 3 ErrX = normal(T) .* 3 rw = kemitor(T,mu,H,F,ErrY,ErrX) rw = vec(1:T)~rw rw = setmask(rw,"line", "blue", "thin") disp = createdisplay(1,1) show(disp,1,1,rw)
Generates a random walk with errors.
library("xplore") library("plot") library("times") randomize(0) T = 100 ErrX = normal(T)~(vec(1:T).*0) ErrY = normal(T).*2 H = 1~0 F = #(0.5,1)~#(-0.3,0) x0 = #(0,0) ar2 = kemitor(T,x0,H,F,ErrY,ErrX) ar2 = vec(1:T)~ar2 ar2 = setmask(ar2,"line", "blue", "thin") disp = createdisplay(1,1) show(disp,1,1,ar2)
Generates an AR(2) with additive gaussian errors.
library("xplore") library("plot") library("times") randomize(0) T = 100 mu = #(20,0) H = #(0.3,-0.3)~#(1,1) F = #(1,0)~#(1,0) ErrY =(normal(T) .* 3)~(normal(T) .* 3) ErrX =(normal(T) .* 0)~(normal(T) .* 3) ser = kemitor(T,mu,H,F,ErrY,ErrX) ser = vec(1:T)~ser ser1 = ser[,1]~ser[,2] ser2 = ser[,1]~ser[,3] ser1 = setmask(ser1,"line", "blue", "thin") ser2 = setmask(ser2,"line", "blue", "thin") disp = createdisplay(2,1) show(disp,1,1,ser1) show(disp,2,1,ser2)
Generates 100 observations of a given state space model.