Sunday, September 18, 2022

Factor Network Autoregressions

 Check this out, by Barigozzi, Cavaliere, and Moramarco:

Very cool methods for dynamic "multilayer networks".  In a standard N-dim net there's one NxN adjacency matrix.  But richer nets may have many kinds of connections, each governed by its own adjacency matrix.  (What a great insight -- so natural and obvious once you hear it.  A nice "ah-ha moment"!)  So perhaps there are K operative NxN adjacency matrices.  Then there is actually a grand 3-dim adjacency matrix (NxNxK) operative -- a cubic rather than a square matrix.  Parsimonious modeling then becomes absolutely crucial, and in that regard BCM effectively propose a modeling framework with a "factor structure" for the set of adjacency matrices.  Really eye-opening.  Lots to think about.     

Saturday, September 3, 2022

Memories of Ted Anderson

Ted is among the very greatest statisticians/econometricians of the 20th-century.  I feel very close to him, as my former Penn colleague, Larry Klein, worked closely with him at Cowles in the 1940s, and another former colleague, Bobby Mariano, was his student at Stanford before coming to Penn around 1970.  I recall a Penn seminar he gave late in his career, on unit moving-average roots.  He started painfully slowly, defining, for example, things like "time series" and "covariance stationarity".  Some eyes were rolling.  Ten minutes later, he was far beyond the frontier.  No eyes were rolling.  Indeed jaws were dropping.  When I visited Stanford in the 1990s for a seminar, he rolled out the red carpet for me.  Amazing, him doing that for me.  What a gentleman.  

Check out this fascinating new take from Peter Phillips:

By:Peter C. B. Phillips (Cowles Foundation, Yale University, University of Auckland, Singapore Management University, University of Southampton)
Abstract:T. W. Anderson did pathbreaking work in econometrics during his remarkable career as an eminent statistician. His primary contributions to econometrics are reviewed here, including his early research on estimation and inference in simultaneous equations models and reduced rank regression. Some of his later works that connect in important ways to econometrics are also briefly covered, including limit theory in explosive autoregression, asymptotic expansions, and exact distribution theory for econometric estimators. The research is considered in the light of its influence on subsequent and ongoing developments in econometrics, notably confidence interval construction under weak instruments and inference in mildly explosive regressions.


Equal-weight HAR combination

This just blows me away.  So full of great insight.  Equal-weight combinations rule, in yet another context!  See also my papers with Minchul Shin that clearly lead to equal weights for point and density forecasts, respectively:

Diebold, F.X. and Shin, M. (2019), "Machine Learning for Regularized Survey Forecast Combination: Partially-Egalitarian Lasso and its Derivatives," International Journal of Forecasting, 35, 1679-1691. 

Diebold, F.X., Shin, M. and Zhang, B. (2022), “On the Aggregation of Probability Assessments: Regularized Mixtures of Predictive Densities for Eurozone Inflation and Real Interest Rates,” Journal of Econometrics, forthcoming.  Working paper at arXiv:2012.11649.

 Forecast combination puzzle in the HAR model

By:Clements, AdamVasnev, Andrey
Abstract:The Heterogeneous Autoregressive (HAR) model of Corsi (2009) has become the benchmark model for predicting realized volatility given its simplicity and consistent empirical performance. Many modifications and extensions to the original model have been proposed that often only provide incremental forecast improvements. In this paper, we take a step back and view the HAR model as a forecast combination that combines three predictors: previous day realization (or random walk forecast), previous week average, and previous month average. When applying the Ordinary Least Squares (OLS) to combine the predictors, the HAR model uses optimal weights that are known to be problematic in the forecast combination literature. In fact, the simple average forecast often outperforms the optimal combination in many empirical applications. We investigate the performance of the simple average forecast for the realized volatility of the Dow Jones Industrial Average equity index. We find dramatic improvements in forecast accuracy across all horizons and different time periods. This is the first time the forecast combination puzzle is identified in this context.
Keywords:Realized volatility, forecast combination, HAR model
JEL:C53 C58

Long memory and weak ID

I've thus far never been a big fan of the weak ID literature.  Always seemed to me that if you wind up with weak ID, it's time to think harder about the underlying economics rather than fancier econometrics.  But this opened my eyes and changed my mind.  Totally cool.  

 Weak Identification of Long Memory with Implications for Inference

By:Jia Li (Singapore Management University); Peter C. B. Phillips (Cowles Foundation, Yale University, University of Auckland, Singapore Management University, University of Southampton); Shuping Shi (Macquarie University); Jun Yu (Singapore Management University)
Abstract:This paper explores weak identification issues arising in commonly used models of economic and financial time series. Two highly popular configurations are shown to be asymptotically observationally equivalent: one with long memory and weak autoregressive dynamics, the other with antipersistent shocks and a near-unit autoregressive root. We develop a data-driven semiparametric and identification-robust approach to inference that reveals such ambiguities and documents the prevalence of weak identification in many realized volatility and trading volume series. The identification-robust empirical evidence generally favors long memory dynamics in volatility and volume, a conclusion that is corroborated using social-media news flow data.
Keywords:Realized volatility; Weak identification; Disjoint confidence sets, Trading volume, Long memory
JEL:C12 C13 C58