Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 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

Example:
```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
disp = createdisplay(1,1)
show(disp,1,1,rw)

```
Result:
```Generates a random walk with errors.
```
Example:
```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
disp = createdisplay(1,1)
show(disp,1,1,ar2)

```
Result:
```Generates an AR(2) with additive gaussian errors.
```
Example:
```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]
disp = createdisplay(2,1)
show(disp,1,1,ser1)
show(disp,2,1,ser2)

```
Result:
```Generates 100 observations of a given state space
model.
```

Author: P.Franek, 19990507
(C) MD*TECH Method and Data Technologies, 05.02.2006