Big data in dynamic predictive econometric modeling

原文摘要

The modern economic environment is awash in Big Data. The business models of many of today’s largest and most innovative firms, for example, are intimately connected to data collection and processing. Closely related, all of science is now similarly awash in Big Data, due to massive advances in data capture and storage technology, typically in conjunction with the internet.1 Time-series econometrics is no exception, and the time-series community is beginning to confront Big Data. Whereas leading texts of a few decades ago like Hamilton (1994) had no mention of Big Data topics, recent texts like Ghysels and Marcellino (2018) cover regularization methods, factor models for large panels, etc. Nevertheless the time-series econometrics of Big Data is still in its infancy, with many important issues explored incompletely or not at all. Against this background, in this volume we present new econometric research at the interface of Big Data and predictive time-series modeling. Topics include, but are not limited to: shrinkage, selection, sparsity, dimensionality reduction, structural change, high-frequency data, mixed-frequency data, and network topology description. A simple taxonomy is useful for understanding the types of Big Data that will concern us, and hence how the volume’s papers relate and cohere. To that end, consider a time-series regression involving T time periods and K regressors, with intra-period sampling m times per period. Then the ‘‘X matrix’’ is mT×K , and Big Data corresponds to situations of very large T , K , and/or m. T , K , and m are usefully considered separately, although more than one can of course be large at once. As T gets large we have ‘‘tall data’’, in reference to the tall X matrix, due to the large number of periods, i.e., the long calendar span of data. As K gets large (potentially even so large that K>T ) we have ‘‘wide data’’, in reference to the wide X matrix due to the large number of regressors. As m gets large we have ‘‘dense data’’, in reference to the high-frequency intra-period sampling, regardless of whether the data are tall. Still maintaining our simple regression motivation, there is nevertheless a fourth source of Big Data: the regression might be multivariate, say N-dimensional. As N gets very large we have ‘‘high-dimensional data’’. More generally we refer to situations involving large N or K , or both, as high-dimensional. (Large K is effectively high-dimensional because endogenizing the regressors in a large-K univariate regression would produce a large-N vector autoregression.) We confront the problem raised by high dimensionality – a small number of degrees of freedom relative to the estimation task at hand – by regularization, that is, by imposing restrictions of one sort or another that allow us to recover some degrees of freedom. The regularization spectrum runs from unconstrained through deterministically constrained. At one end is completely unconstrained estimation. Next comes stochastically constrained estimation; that is, with estimates coaxed in a certain direction without being forced. We speak of ‘‘shrinkage’’, and shrinkage strength can of course vary. (In a Bayesian interpretation, shrinkage is toward the prior mean, with strength governed by prior precision.) In the limit we have deterministic restrictions such as exact zeros, promoting sparsity and variable selection, and other restrictions such as reduced rank, associated with factor structure and cointegration.2 Many of the papers in this volume involve large K and/or N and proceed via some sort of shrinkage-type regularization. Examples include Billio, Casarin, and Rossini, ‘‘Bayesian Nonparametric Sparse Vector Autoregressive Models’’; Carriero, Clark and Marcellino, ‘‘Large Bayesian Vector Autoregressions with Stochastic Volatility and Non-Conjugate Priors’’; and Chen, Li, and Linton, ‘‘A New Semiparametric Estimation Approach of Large Dynamic Covariance Matrices with Multiple Conditioning Variables’’.

摘要来源：Semantic Scholar