Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons

Barbara Rossi and Elena Pesavento

No 4536, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this Paper is to propose a simple method for constructing confidence bands for impulse response functions that is not pointwise and that is robust to the presence of highly persistent processes. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead time of the impulse response function to be a fixed fraction of the sample size. These devices provide better approximations in small samples. Monte Carlo simulations show that our method tends to have better coverage properties at long horizons than existing methods. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. Applications to real GDP and to nominal versus real sources of fluctuations in exchange rates are discussed.

Keywords: Local to unity asymptotics; Persistence; Impulse response functions; Vars (search for similar items in EconPapers)
JEL-codes: C12 C32 F40 (search for similar items in EconPapers)
Date: 2004-09
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Small-sample confidence intervals for multivariate impulse response functions at long horizons (2006)
Working Paper: Small sample confidence intervals for multivariate impulse response functions at long horizons (2004)
Working Paper: Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons (2003)
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