What's a time series model for forecasting a percentage bound by (0,1)? This must come up---the forecasting of things that are stuck between 0 and 1.
In my series, I suspect an auto-regression component, and also a mean-reverting component, so I want something that I can interpret like an ARIMA---but I don't want it to shoot off to 1000% in the future.
Do you just use an ARIMA model as the parameter in a logistic regression to confine the result between 0 and 1?
Or I learned here that Beta regressions are more appropriate for (0,1) data.  How would I apply this to a time series?  Are there good R packages or Matlab functions that make fitting and forecasting this easy?
 A: In my PhD Dissertation at Stanford in 1978 I constructed a family of first order autoregressive processes with uniform marginal distributions on $[0,1]$  For any integer $r\geq 2$ let $X(t) = X(t-1)/r+e(t)$ where $e(t)$ has the following discrete uniform distribution that is $P(e(t) = k/r)=1/r$ for $k=0,1,..., r-1$.  It is interesting that even though $e(t)$ is discrete each $X(t)$ has a continuous uniform distribution on $[0,1]$ if you start out assuming $X(0)$ is uniform on $[0,1]$.  Later Richard Davis and I extended this to negative correlation i.e. $X(t) =-X(t-1)/r + e(t)$.  It is interesting as an example of a stationary autoregressive time series constrained to vary between $0$ and $1$ as you indicated you are interested in.  It is a slightly pathological case because although the maximum of the sequences satisfies an extreme value limit similar to the limit for IID uniforms it has an extremal index less than $1$.  In my thesis and Annals of Probability paper I showed that the extremal index was $(r-1)/r$.  I didn't refer to it as the extremal index because that term was coined later by Leadbetter (most notably mentioned in his 1983 Springer text coauthored with Rootzen and Lindgren).  I don't know if this model has much practical value.  I think probably not since the noise distribution is so peculiar.  But it does serve as a slightly pathological example.
A: I asked this a long time ago but SO just popped it back up.  In the case I was looking at, I ended up forecasting numerator and denominator separately, which made more sense for the metric anyway.
