Focused information criterion for locally misspecified vector autoregressive models

Abstract

This paper investigates the focused information criterion and plug-in average for vector autoregressive models with local-to-zero misspeci cation. These methods have the advantage of focusing on a quantity of interest rather than aiming at overall model t. Any (su ciently regular) function of the parameters can be used as a quantity of interest. We determine the asymptotic properties and elaborate on the role of the locally misspeci ed parameters. In particular, we show that the inability to consistently estimate locally misspeci ed parameters translates into suboptimal selection and averaging. We apply this framework to impulse response analysis. A Monte Carlo simulation study supports our claims.

The Focused Information Criterion for Stochastic Model Selection Problems Using $M$-Estimators

“…Hence, albeit biased, a plug-in estimator may be preferred over an asymptotically unbiased estimator. Lohmeyer et al (2018) give an account of the impacts of both these estimators on performance of FIC.…”

“…The other instance of using non-likelihood estimators for focused model selection is provided by Lohmeyer et al (2018) who construct FIC using least square estimators for selection problems for vector autoregressive models. Least square estimators are indeed M -estimators with the squared residual function being the criterion function to be minimized.…”

“…Although we present the results for univariate stochastic process, it should be possible to extend the functional asymptotics and consequently the parametric inference to the case of vector valued stochastic processes. Hence, it is possible to view the theory of Lohmeyer et al (2018) as special case of our setup.…”

A Unified Approach to Focused Information Criterion and Plug-In Averaging Method

“…Since the seminal work of Claeskens and Hjort (2003), the FIC has been investigated in different models, including the Cox hazard regression model (Hjort and Claeskens, 2006), the general semiparametric model (Claeskens and Carroll, 2007), the generalized additive partial linear model (Zhang and Liang, 2011), the varying-coefficient partially linear measurement er-ror model (Wang, Zou, and Wan, 2012), the Tobin model with a nonzero threshold (Zhang, Wan, and Zhou, 2012), the partially linear single-index model (Yu et al, 2013), the linear mixed-effects model (Chen, Zou, and Zhang, 2013), generalized empirical likelihood estimation (Sueishi, 2013), the graphical model (Pircalabelu, Claeskens, and Waldorp, 2015), propensity score weighted estimation of the treatment effects (Lu, 2015;Kitagawa and Muris, 2016), the choice between parametric and nonparametric models (Jullum and Hjort, 2017), generalized method of moments estimation (DiTraglia, 2016;Chang and DiTraglia, 2018), vector autoregressive models (Lohmeyer et al, 2019), and others. It is well known that many of these estimators share a common structure, which is useful in deriving the FIC in different model setups.…”