Mihael - 1 month ago 10

R Question

Is there a way to specify minimum or maximum possible values in a forecast done with ETS/ARIMA models?

Such as when forecasting a trend in % that can only go between 0% and 100%.

I am using R package

`forecast`

`forecast`

Answer

If your time series `y`

has a natural bound `[a, b]`

, you should take a "logit-alike" transform first:

```
f <- function (x, a, b) log((x - a) / (b - x))
yy <- f(y, a, b)
```

Then the resulting `yy`

is unbounded on `(-Inf, Inf)`

, suitable for Gaussian error assumption. Use `yy`

for time series modelling, and take back-transform later on the prediction / forecast:

```
finv <- function (x, a, b) (b * exp(x) + a) / (exp(x) + 1)
y <- finv(yy, a, b)
```

Note, the above transform `f`

(hence `finv`

) is monotone, so if the 95%-confidence interval for `yy`

is `[l, u]`

, the corresponding confidence interval for `y`

is `[finv(l), finv(u)]`

.

If your `y`

is only bounded on one side, consider "log-alike" transform.

- bounded on
`[a, Inf)`

, consider`yy <- log(y - a)`

; - bounded on
`(-Inf, a]`

, consider`yy <- log(a - y)`

.

Wow, I didn't know Rob Hyndman has a blog. Thanks to @ulfelder for providing it. I added it here to make my answer more solid: Forecasting within limits.

This one is more specific, which I have not covered. What to do when data need a log transform but it can take 0 somewhere. I would just add a small tolerance, say `yy <- log(y + 1e-7)`

to proceed.