Question: I'm building a model which predicts the GDP(Quarterly) of my country. I've lots of time-series predictors(~50(Monthly), all continuous, e.g. Index of Industrial Production, etc.) but my dataset size is small(~120). I've tried using ARIMA(5,1,0) on GDP values: [![enter image description here](https://i.stack.imgur.com/fa79I.png)](https://i.stack.imgur.com/fa79I.png)

I'm looking for a model which could take into account how predictors affect GDP along with past GDP values.

Should I try using Recurrent Neural Nets on such small dataset? 

Also, I used log-transform to account of increasing variance in GDP values, which still hasn't solved the issue completely. Any suggestions on how to solve this would be amazing.

I'm using Python.

Answer: 
Your focal time series and the "predictors" are interrelated. You might as well want to forecast the Index of Industrial Production, using GDP as a "predictor".

The classical approach to such a problem is [Vector Autoregression (VAR)](https://en.wikipedia.org/wiki/Vector_autoregression), which models - and forecasts - the relationships *between* your series, as well as the time dynamics.

Such problems are the bread and butter of econometricians. I suggest you pick up pretty much any econometric textbook, perhaps looking for one that uses software you are comfortable with, such as Python.
it appears to me that the error variance changed deterministically at two points in time . See <http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html> . I was responsible for seamlessly integrating this along with Intervention Detection into a commercial package that I helped to develop. The implementation was for both ARIMA and Transfer Function (causal) Models.

Whereas the Box-Cox test [When (and why) should you take the log of a distribution (of numbers)?](https://stats.stackexchange.com/questions/18844/when-and-why-should-you-take-the-log-of-a-distribution-of-numbers/18852#18852) remedies a linkage between the expected value and the variance, the TSAY test leads to GLS .