I am working with time series values which are all in the closed interval [0, 1]; these values represent relative frequencies, i.e., empirical probabilities. I would like to create a model such that all forecasted values are within [0, 1], but it would also be fine if the model's output was strictly within the open interval (0, 1).

This answered question tackles the lower bound aspect of my question, but not the upper bound aspect: How to achieve strictly positive forecasts?

I'd like to use the R forecast package if possible to achieve this, but I am open to other suggestions.

  • $\begingroup$ May be time series logistic regression. I have not personally applied it, but I have come across in couple of instances in this website. $\endgroup$
    – forecaster
    Commented Jul 14, 2014 at 1:04
  • 2
    $\begingroup$ See robjhyndman.com/hyndsight/forecasting-within-limits $\endgroup$ Commented Jul 14, 2014 at 3:57
  • $\begingroup$ Prof. Hyndman, thank you for the clarification and for the forecast package! $\endgroup$ Commented Jul 14, 2014 at 12:46

1 Answer 1


Prof. Hyndman points out this approach in his comment above:

"...trans­form the data using a scaled logit trans­form which maps (a,b) to the whole real line:

$$y = \log\left(\frac{x-a}{b-x}\right)$$

where x is on the orig­i­nal scale and y is the trans­formed data."

See: http://robjhyndman.com/hyndsight/forecasting-within-limits/


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