Sparse seemingly unrelated regression modelling: Applications in finance and econometrics

Bayesian Analysis of Latent Threshold Dynamic Models

“…The standard use of sparsity priors for regression model uncertainty and variable selection McCulloch 1993, 1997;Clyde and George 2004) has become widespread in areas including sparse factor analysis Carvalho et al 2008;Yoshida and West 2010), graphical modeling (Jones et al 2005), and traditional time series models (e.g., George et al 2008;Chen et al 2011). In the context of time series analysis, these general strategies have been usefully applied to induce "global" shrinkage to zero of parameter subsets, zeroing out regression coefficients in a time series model for all time (Carvalho and West 2007;George et al 2008;Korobilis 2012;Wang 2010). The LTM mechanism builds on this idea but addresses the much more general question of time-varying inclusion of effects, i.e., dynamic sparsity modeling.…”

“…With increasing variables in the VAR, the number of coefficients in autoregressive coefficient matrices escalates as does the need for parameter constraints. Recent Bayesian VAR analysis addresses this using shrinkage and sparsity-inducing priors of various forms (Fox et al 2008;George et al 2008;Wang 2010) for traditional constant coefficient VAR models, but the induction of zeros into increasingly sparse time-varying coefficient matrices, with allowance for time-variation in the occurrence of non-zero values as well as local changes in coefficients when they are non-zero, has been challenging; the LTM ideas provide an approach.…”

Dynamic network signal processing using latent threshold models

“…Coupled with this is the now traditional use of Bayesian graphical modelling to induce zeros in precision matrices of innovations in TV-VAR and other dynamic models (e.g. [5,41,40]). The concept and resulting methodology of latent threshold modelling is a very general, and widely applicable strategy that permits the existence of relationships to vary over time, i.e., allowing time-and data-adaptive dynamics in sparsity patterns in all model components within an overall model structure.…”

Variable Selection in Seemingly Unrelated Regressions with Random Predictors

“…Indeed, such joint regression models go by the name "seemingly unrelated regressions" (SUR) in the Bayesian econometrics literature, reflecting the fact that the regression coefficients from each of the separate regressions can be obtained in isolation from one another (i.e., conducting estimation as if Ψ were diagonal). However, allowing non-diagonal Ψ can lead to more efficient estimation (Zellner, 1962) and can similarly impact variable selection (Brown, Vannucci and Fearn, 1998;Wang, 2010). This paper differs from Brown, Vannucci and Fearn (1998) and Wang (2010) in that we focus on the case where the predictor variables (the regressors, or covariates) are treated as random as opposed to fixed.Our goal will be to summarize codependence among multiple responses in subsequent periods, making the uncertainty in future realizations highly central to our selection objective.…”

“…However, allowing non-diagonal Ψ can lead to more efficient estimation (Zellner, 1962) and can similarly impact variable selection (Brown, Vannucci and Fearn, 1998;Wang, 2010). This paper differs from Brown, Vannucci and Fearn (1998) and Wang (2010) in that we focus on the case where the predictor variables (the regressors, or covariates) are treated as random as opposed to fixed.Our goal will be to summarize codependence among multiple responses in subsequent periods, making the uncertainty in future realizations highly central to our selection objective. This approach is natural in many contexts (e.g., macroeconomic models) where the purpose of selection is inherently forward-looking.…”