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.
There is a lot of literature on nowcasting in general, and GDP in particular. For instance, check [GDPNow page](https://www.frbatlanta.org/cqer/research/gdpnow.aspx) on FRB Atlanta's web site, where the model description is given too. Below is their 2017 Q4 GPD forecast. As you know the GDP number release will be some time in 2018, i.e. a few months down the road from the time I'm posting my ansqwer.
[![enter image description here](https://i.stack.imgur.com/wlKPa.gif)](https://i.stack.imgur.com/wlKPa.gif)

Nowcasting is used to estimate the low frequency data based on high frequency predictors. For instance, CPI and Unemployment are released monthly, the interest rates are available either real time or at least daily. You could use these as predictors to estimate GDP between its quarterly releases. 

Nowcasting is different from ordinary time series forecasting in that it has no issue with predicting the predictors. For instance, if you were to predict GDP one year ahead, you'd need values of its predictors one year ahead.