Suppose we have count data. It seems that a generalized ARMA model would be good to use. In Rm these is function:
garma(link = c("identity", "loge", "reciprocal", "logit", "probit", "cloglog", "cauchit"), earg=list(), p.ar.lag = 1, q.lag.ma = 0, coefstart = NULL, step = 1)
Why type of link function would be good to use? There is no poisson option.
There are integer valued AR processes that have been developed with some theory behind them. My colleague Jan Sun just did her PhD dissertation on this topic at the University of Liverpool Economics Department. Her thesis might be one good place to find references. There was a conference on this topic in Cyrus last year.
Here is a presentation by Richard Davis from 2001: http://www.stat.columbia.edu/~rdavis/lectures/montreal.pdf
Some more articles:
http://polisci.osu.edu/faculty/jbox/Courses/ps8125/brandtslides.pdf
https://dspace.lboro.ac.uk/dspace-jspui/handle/2134/5308
http://monogan.myweb.uga.edu/teaching/ts/mediaCount_v7.pdf
http://ideas.repec.org/p/zbw/cauewp/3194.html
http://personal.fmipa.itb.ac.id/khreshna/files/2011/02/brannas1995.pdf
http://wires.wiley.com/WileyCDA/WiresArticle/wisId-WICS47.html
http://sankhya.isical.ac.in/search/71b2/paper_7.pdf
A reference on the conferene that I mentioned: http://www2.ucy.ac.cy/~wints2011/
The first conference that came before the one above
