# [R] stochastic process transition probabilities estimation

Massimo Santini santini at dsi.unimi.it
Tue Apr 4 13:41:41 CEST 2000

```Hi all,
I'm new with R (and S), and relatively new to statistics (I'm a
computer scientist), so I ask sorry in advance if my question is silly.

My problem is this: I have a (sample of a) discrete time stochastic
process {X_t} and I want to estimate

Pr{ X_t | X_{t-l_1}, X_{t-l_2}, ..., X_{t-l_k} }

where l_1, l_2, ..., l_k are some fixed time lags. It will be enough for
me to compute

#{ X_t=a_t, X_{t-l_1}=a_{t-l_1}, X_{t-l_2}=a_{t-l_2}, ..., X_{t-l_k}=a_{t-l_k} }
----------------------------------------------------------------------------------
#{ X_{t-l_1}=a_{t-l_1}, X_{t-l_2}=a_{t-l_2}, ..., X_{t-l_k}=a_{t-l_k} }

for any given sequence of a_t, a_{t-l_1}, a_{t-l_2}, ..., a_{t-l_k}.

If I should do this in C, Fortran or some other algol-like programming language
I've no doubt it will take to me no more than few minutes to write down the code.

But I'm interested in doing it within R framework in order to further
use such a result in a statistical context, where other powerfull
tools are available. Shurly I can try to implement an external
function and use it with R, but this probably wouldn't be as simple as
to write the code in R itself.

An idea should be to use R in a "multivariate" fashion: if I can get
factors of a multivariate random variable, I can build a random vector
Y_t using X_t, and its lags: Y_t = [ X_t, X_{t-l_1}, X_{t-l_2}, ...,
X_{t-l_k} ], and taking the factors of Y_t and of its margin without
the first component I think I'm done.  Unfortunately, factor, sort,
unique all work only with univariate data.

Any other suggestion will be very appreciated...

Best regards, Massimo

--
Dr.  Massimo Santini
Tel. Milano +390255006278, Crema +390373898227;  Fax. +390255006373
<mailto:santini at dsi.unimi.it> <http://zorn.usr.dsi.unimi/~santini/>

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```