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: 
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.
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 .