Big Data in Dynamic Predictive Modeling

Our Journal of Econometrics issue, Big Data in Dynamic Predictive Econometric Modeling, is now in press.  It is partly based on a Penn conference, generously supported by Penn's Warren Center for Network and Data Sciences, University of Chicago's Stevanovich Center for Financial Mathematics, and Penn's Institute for Economic Research.  The intro is here and the paper list is here.

Network Tools for Understanding High-Dimensional Dynamic Models

The slides from my "overview" IMF talk two weeks ago proved popular, so here are some different overview slides on a different topic ("Estimating and Understanding High-Dimensional Dynamic Stochastic Econometric Models"), from my talk at last week's NYU Stern Conference on Volatility and Derivatives.

Statistical Machine Learning Circa 1989

I've always been a massive fan of statisticians whose work is rigorous yet practical, with emphasis on modeling. People like Box, Cox, Hastie, and Tibshirani obviously come to mind.  So too, of course, do Leo Brieman and Jerry Friedman.  

I had the good luck to stumble into a week-long intensive lecture series with Jerry Friedman in 1989, a sort of summer school for twenty-something assistant professors and the like.  At the time I was a young economist in DC at the Federal Reserve Board, and the lectures were just down the street at GW.

I thought I would attend to learn some non-parametrics, and I definitely did learn some non-parametrics.  But far more than that, Jerry opened my eyes to what would be unfolding for the next half-century -- flexible, algorithmic, high-dimensional methods -- the statistics of "Big Data" and "machine learning".  

I just found the binder containing his lecture notes.  The contents appear below.  Read the opening overview, "Modern Statistics and the Computer Revolution".  Amazingly prescient.  Remember, this was 1989!

[Side note:  There I also had the pleasure of first meeting Bob Stine, who has now been my esteemed Penn Statistics colleague for more than 25 years.]

Time-Varying Dynamic Factor Loadings

Check out Mikkelsen et al. (2015).  I've always wanted to try high-dimensional dynamic factor models (DFM's) with time-varying loadings as an approach to network connectedness measurement (e.g., increasing connectedness would correspond to increasing factor loadings...).  The problem for me was how to do time-varying parameter DFM's in (ultra) high dimensions.  Enter Mikkelsen et al.  I also like that it's MLE -- I'm still an MLE fan, per Doz, Giannone and Reichlin.  It might be cool and appropriate to endow the time-varying factor loadings with factor structure themselves, which might be a straightforward extension (application?) of Sevanovic (2015).  (Stevanovic paper here; supplementary material here.)

Maximum Likelihood Estimation of Time-Varying Loadings in High-Dimensional Factor Models

Jakob Guldbæk Mikkelsen (Aarhus University and CREATES) ; Eric Hillebrand (Aarhus University and CREATES) ; Giovanni Urga (Cass Business School)

2015

In this paper, we develop a maximum likelihood estimator of time-varying loadings in high-dimensional factor models. We specify the loadings to evolve as stationary vector autoregressions (VAR) and show that consistent estimates of the loadings parameters can be obtained by a two-step maximum likelihood estimation procedure. In the first step, principal components are extracted from the data to form factor estimates. In the second step, the parameters of the loadings VARs are estimated as a set of univariate regression models with time-varying coefficients. We document the finite-sample properties of the maximum likelihood estimator through an extensive simulation study and illustrate the empirical relevance of the time-varying loadings structure using a large quarterly dataset for the US economy.