# Fully endogenous models for predicting multivariate time series

I have a formal social science background but I am new to data science. My interest is in building predictive models for applications in the social sciences, mostly (but not only) in economics.

I am interested in the following kind of setups:

• I have data that describe the evolution of a number of variables $$j \in J$$ for a number of "individuals" $$i\in N$$ across time periods $$t \in \{1\dots, T\}$$.
• For example, "individuals" $$i\in N$$ could be countries, with $$j=1$$ being GDP, $$j=2$$ inflation, $$j=3$$ interest rate, $$j=4$$ unemployment rate, etc, although in practice I would look at situations where $$\#N > 195$$ (maybe $$i\in N$$ would be regions, or counties, rather than countries).
• As the above example suggests, I am interested in situations where all my variables of interest are likely to be related to one another.
• I am looking for models that, based on data for $$t\in \{1,\dots, T\}$$ can forecast the co-movement of all my variables of interest for $$t > T$$ (at least a couple of periods ahead). In particular, I don't want to have to assume some particular future scenario for all but one variable in order to get a prediction about the last one.
• I am interested in prediction only, not in satistically interpreting my model.

Being trained as an economist, I know that Vector Autoregression (VAR) is one option for such "fully endogeneous" models. I have tried to learn a little more about forecasting and time-series (e.g., read through https://otexts.org/fpp2) but found little alternatives to VAR so far. Now, VAR might be fine and it might be the only option out there. But I would like to know if there are alternatives modeling techniques one may want to consider for these kinds of problems.

My questions:

1. What would be some alternative to VAR be to tackle these kinds of endogenous prediction problems (if any)?
2. Are there any resources where the application of these alternative techniques would be discussed specifically in this context?
• One of the simplest things you can do is run correlations between all your quantitative variables. If you have a very high correlation between, say, $X$ and $Y,$ then just eliminate one of them. – Adrian Keister Sep 27 '18 at 13:52

## 1 Answer

I am still interested in alternatives that depart more fundamentally from VAR, but digging a little deeper, I found some interesting variations around VAR that I did not know about and could be very useful.

Of particular interest are regularized VAR models. Applications to macroeconomic forecasting are for example discussed here: https://arxiv.org/abs/1508.07497.

Even better, the paper comes with a fully funcitonal R-package: https://cran.r-project.org/web/packages/BigVAR/index.html, that is described in more details here: https://arxiv.org/abs/1702.07094.

Some of the regularized method in the package, like VARX-L, allows for exogenous variables. As I described in my answer, this is not what I am directly interested in. But VARX-L (and the BigVar package) only allow for exogenous variables and do not require the inclusion of such variables (the exogenous channel can be shut down with the model still being operational). Good to know I can start with a fully endogenous model and have to flexibility to add exogenous variables later if needed.