DSGE models aim to be explanatory models of an economy. They are not the best at predicting (bayesian VARs do better forecasting, there is a tutorial on it in my quant econ link) but they turn out to do forecasting decently well, too.
The reason that is is that purely statistical/predictive models of macro are subject to the Lucas Critique [1]. It says roughly, if you observe an economic relationship is happening, but you don't have an explanatory reason why it is, it's a bad idea to use it for policy prescription.
The NY fed model has a whitepaper here [2], which should be accessible to the technical data scientist (technical, but not prohibitively so).
Their readme points to a few posts on using it, I think the open source code comes with a csv for example input data. There should be publicly accessible macroeconomic data in a few places for you to play with it, say at FRED or the World Bank. I think Julia has a Stata-style api package for FRED data, making the data processing easier.
The foundation DSGE models are nothing like regular statistical or machine learning models. They are general equilibrium models, a type of mathematical model the falls under the microeconomics area of economics.
DSGE try to predict how an economical system will evolve over time, given agents preferences, technologies and institutions, how much will be produced, consumed, traded, prices and how those behave over time, taking into account stochastic impacts, like idk oil price fluctuation.
They are beautiful theoretically, since they are micro constructed. See, economists don't like to use aggregates only to make predictions and infer policy impacts due to something called Lucas critique ( https://en.wikipedia.org/wiki/Lucas_critique ) which basically means that taking an inflation series create an ARIMA(x,y,z) to predict next weeks CPI is theoretically. invalid.
The estimation however, is usually based on Bayesian hierarchical models, taking the constraints imposed by the theoretical model, I believe.
DSGE have been criticized for their low predictive power, but it can be said that in that for mid to long term predictions they are more robust for monetary and fiscal policy use.
Is there some way to play with these models? Or do you need lots of input data, which isn't freely available?