Thank you very much for clearing my question (for me too ;))
The model I would like to fit is :
X_t = phi_1 * X_{t-1} + phi_2 * X_{t-2}
+ phi_3 * X_{t-3} +
A_1*f_{t-1}+A_2*f_{t-2}...+A_k*f_{t-k} + E_t (*)
(X_t and f_t time series are both known, k - fixed and more than 1).
lm is a good answer (I surely try it), but I thought may be somethere in
R exists a front-end to lm for this particular case. For example if I
have a model
X_t = phi_1 * X_{t-1} + phi_2 * X_{t-2}
+ phi_3 * X_{t-3} + E_t (**), I would use
an "ar" command from "stats" package. My problem is how to make my model
(*) suit "ar" command (may model (*) be rewritten in (**) form)?
Rolf Turner wrote:
It is not at all clear what you want to do. One conjecture
(attempt at reading your mind):
X_t = ``black box's state'' at time t
f_t = ``force'' at time t
Proposed model e.g. AR(3):
X_t = phi_1 * X_{t-1} + phi_2 * X_{t-2}
+ phi_3 * X_{t-3} + f_t
You wish to identify/estimate the coefficients phi_1, phi_2,
phi_3.
Remarks:
(a) This model probably doesn't make a lot of sense, with
known/observed f_t. It will almost surely not hold exactly,
for ***any*** values of the phi_i.
(b) A model which makes a bit more sense, in the abstract, is
X_t = phi_1 * X_{t-1} + phi_2 * X_{t-2}
+ phi_3 * X_{t-3} + f_t + E_t
where E_t is (unobserved) i.i.d. random ``error''.
(c) This last model is just a simple regression model and
may be fitted using lm().
cheers,
Rolf Turner
[EMAIL PROTECTED]
Original message:
Hello!
Is it possible to use R time series to identificate a process which is
subjected to known input? I.e. I have 2 sequences - one is measurements
of black box's state and the second is the "force" by which this black
box is driven (which is known too) and I want to fit thist two series
with AR-process. The "ar" procedure from stats package expects that the
force is always random. Is it possible to feed it known vector as input
parameter?
Thank you in advance.
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