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: genarma Description: generates an autoregressive moving average process (ARMA) in deviations from the mean form y_t = a(B)y_t + eps_t + b(B)eps_t B denotes the backshift (or lag) operator. You have to deliver the AR coefficients vector a, the MA coefficients vector b and the (T x 1) white noise series eps. The output y is a (T x 1) ARMA series. The simulation routine sets the necessary initial values to 0 (that is y_t=eps_t=0 for t<1).

Reference(s):
Hamilton, James D. (1994): Time Series Analysis. Princeton (Princeton University Press), pp.59-61. Mills, Terence C. (1990): Time Series Techniques for Economists. Cambridge (Cambridge University Press), pp. 63-91.

 Usage: y = genarma(a,b,eps) Input: a (p x 1) vector of AR coefficients b (q x 1) vector of MA coefficients eps (T x 1) vector of white noise disturbances Output: y (T x 1) vector with the generated ARMA process

Example:
```library("times")    ; loads the quantlets from times library
randomize(0)        ; sets the seed
y = genarma(0.5,0.5,normal(1000))
pacfplot(y,12)     ; display of the sample pacf for y_t
acfplot(y,12)      ; display of the sample acf for y_t

```
Result:
```Two displays that show the acf and the pacf of the
generated ARMA(1,1) process y_t. The series y has
T=1000 observations. The displays resemble the exhibits
in Mills (cited above), p. 89.
```

Author: C. Hafner, W. Haerdle, R. Schulz, 20010501 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006