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Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR(∞) Models*
Author(s) -
Inoue Atsushi,
Kilian Lutz
Publication year - 2002
Publication title -
international economic review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.658
H-Index - 86
eISSN - 1468-2354
pISSN - 0020-6598
DOI - 10.1111/1468-2354.t01-1-00016
Subject(s) - bootstrapping (finance) , autoregressive model , mathematics , heteroscedasticity , estimator , vector autoregression , econometrics , impulse response , variance (accounting) , residual , inference , statistics , computer science , economics , algorithm , mathematical analysis , accounting , artificial intelligence
It is common to conduct bootstrap inference in vector autoregressive (VAR) models based on the assumption that the underlying data‐generating process is of finite‐lag order. This assumption is implausible in practice. We establish the asymptotic validity of the residual‐based bootstrap method for smooth functions of VAR slope parameters and innovation variances under the alternative assumption that a sequence of finite‐lag order VAR models is fitted to data generated by a VAR process of possibly infinite order. This class of statistics includes measures of predictability and orthogonalized impulse responses and variance decompositions. Our approach provides an alternative to the use of the asymptotic normal approximation and can be used even in the absence of closed‐form solutions for the variance of the estimator. We illustrate the practical relevance of our findings for applied work, including the evaluation of macroeconomic models.