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.

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#### Best Answer

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:

$$y = logleft(frac{x-a}{b-x}right)$$

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

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