# 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?

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

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

-
If there is a positive trend in your time-series and the “auto.arima” function captured the trend, perhaps by first-differencing and including a mean or a drift term in the model, one would expect forecasts to be larger than historic data. –  RioRaider Aug 7 '12 at 17:21
I've added max.p = 1, max.q = 1, max.P = 0 and max.Q = 0. It reduces a bit, but still high. –  Fernando Aug 7 '12 at 17:26
I agree with RioRaider. How do you know that the forecasts should not be higher than historical values? An automatic ARIMA model builder will use first or second differences to handle linear or quesdratic trends respectively. If there are historical trends it would be appropriate to project them into the future unless you have external knowledge about the process that indicates something to the contrary. –  Michael Chernick Aug 7 '12 at 17:30
@Fernando Instead of playing with the input parameters to try to reduce the forecast why not look at the fitted model to get an idea of why it is trending up. Does an uptrend show in the historical data? Did the model include a first or second difference operation? –  Michael Chernick Aug 7 '12 at 17:33
Thanks for the feedback. I'm actually new to time series/forecasting. My model says ARIMA(2,1,0)(2,0,1)[12], and yes there is a small positive trend. A simple linear regression gives me more reasonable forecasts...is there some way to tweak the ARIMA model, to avoid these high-values? –  Fernando Aug 7 '12 at 20:41

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: