I am working on a time series whose values are

strictly positive. Working with various models including AR, MA, ARMA, etc, I couldn’t find an easy way to achieve strictly positive forecasts.I’m using

Rfor doing my forecasts, and all that I could find was forecast.hts {hts} that has apositiveparameter described here:

Forecast a hierarchical or grouped time series, package hts`## S3 method for class 'gts': forecast((object, h, method = c("comb", "bu", "mo", "tdgsf", "tdgsa", "tdfp", "all"), fmethod = c("ets", "rw", "arima"), level, positive = FALSE, xreg = NULL, newxreg = NULL, ...)) positive If TRUE, forecasts are forced to be strictly positive`

http://www.inside-r.org/packages/cran/hts/docs/forecast.gts

Any suggestions for non-hierarchical time series? What about generalization on using other constraints like minimum, maximum, etc?

Even if not implemented in R, suggestions on articles, models or helpful general variable transformations would be appreciated.

**Answer**

With the `forecast`

package for R, simply set `lambda=0`

when fitting a model. For example:

```
fit <- auto.arima(x, lambda=0)
forecast(fit)
```

Many of the functions in the package allow the `lambda`

argument. When the `lambda`

argument is specified, a Box-Cox transformation is used. The value λ=0 specifies a log transformation. So setting `lambda=0`

means the logged data are modelled, and when forecasts are produced, they are back-transformed to the original space.

See http://www.otexts.org/fpp/2/4 for further discussion.

**Attribution***Source : Link , Question Author : Ho1 , Answer Author : Rob Hyndman*