# Arima model giving high forecast values

I have some models built with the auto.arima function from the forecast package. I’m modeling a variable called ‘natural efluent energy’ (ena), which is how much energy you can extract from some Hydrography region. There are 2 regressor variables (rainfall precipitation from period $t$ and $t-1$.)

Each region has it’s own model – some series show positive trend, some shows negative trend, and some seems stationary. The problem is that some forecasts ‘from auto.arima‘ are giving values higher/lower than usual (some forecasts give me negative values, which are not possible).

My original call is below:

 m1 = auto.arima(serie, xreg = regvars)


For the data on the link, I changed it to

 m1 = auto.arima(serie, xreg = regvars, max.P = 0, max.Q = 0, stationary = TRUE)


Then I get good forecasts in this case. My question is, what these parameters(max.P, max.Q) actually control, and how they relate to the trend show by my model variable?

Here is a link for the historic data:

And here a link for the forecast regressors:

And here a link of mean historic values, the forecast must fall between these values:

My data starts at 2001/Jun, so the serie is:

  y = ts(dframe\$ena, freq = 12, start = c(2001, 6))


Cross Validated Asked on December 27, 2020

If a series is growing then the forecasts will exceed the history. In all probability the model you are using is perhaps inappropriate as outliers/inliers, level/step shifts , seasonal pulses and or local time trends may be present. I don't believe these are accounted for in the automatic model identification process but I could be wrong and their omission can easily thwart ARIMA model identification and consequently forecasting. Furthermore changes in parameters or changes in variance over time are not accounted for and can have negative effects on parameter estimation and subsequently forecasting.

AFTER RECEIPT OF DATA:

Correct answer by IrishStat on December 27, 2020

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