Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|improve this question
I might begin by estimating a logit/probit type model by including the lags . However, I believe there are issues with correcting for autocorrelation in these types of models, so I would hesitate to draw any statistical inferences. – John May 29 '12 at 21:16

In my PhD Dissertation at Stanford in 1978 I constructed a family of first order autoregression process withe 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 the OP indicated he is 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.

share|improve this answer
up vote 0 down vote accepted

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.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.