On 26/04/2009, at 3:56 PM, Rebecca1117 wrote:
>
> I am new in R.
>
> I can simulate Arma, using Arima.sim
>
> However, I want to simulate an Arima Model. Say (1-B)Zt=5+(1-B)at.
> I do not
> know how to deal with 5 in this model.
>
> Can any one could help me?
> Thank you very much!
If this is a homework problem your instructor needs to learn some
time series!
The specific model that you have stated is ill-defined. First of all
note that
Z_t cannot be stationary in mean, otherwise you'd have mu - mu = 5,
or 0 = 5,
which is not true!
If you assume that E(Z_t) = mu_t you get mu_t = 5 + mu_{t-1} so mu_t
= 5t + mu_0.
So you ``could'' (but wait a bit, you can't!) generate say W_t
according to
(1-B)W_t = (1-B)a_t and then set Z_t = W_t + 5t + mu_0 (for any mu_0
that you like).
But the problem is that the (1-B) ``cancels'' in the W_t model so the
W_t are
not well-defined. You need to get it clearer what you want to do.
Note that in general having (1-B) terms in the coefficient of a_t is
to be
avoided. This makes the model non-invertible which implies problems
with
forecasting.
For a ***stationary*** ARMA model phi(B)Z_t = phi_0 + theta(B)a_t you
could
generate W_t according to phi(B)W_t = theta(B)a_t and then set
Z_t = W_t + mu
where mu = phi_0/phi(1).
HTH
cheers,
Rolf Turner
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