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Automatic Inference For Infinite Order Vector Autoregressions

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  • Kuersteiner, Guido M.

Abstract

Infinite order vector autoregressive (VAR) models have been used in a number of applications ranging from spectral density estimation, impulse response analysis, and tests for cointegration and unit roots, to forecasting. For estimation of such models it is necessary to approximate the infinite order lag structure by finite order VARs. In practice, the order of approximation is often selected by information criteria or by general-to-specific specification tests. Unlike in the finite order VAR case these selection rules are not consistent in the usual sense, and the asymptotic properties of parameter estimates of the infinite order VAR do not follow as easily as in the finite order case. In this paper it is shown that the parameter estimates of the infinite order VAR are asymptotically normal with zero mean when the model is approximated by a finite order VAR with a data dependent lag length. The requirement for the result to hold is that the selected lag length satisfies certain rate conditions with probability tending to one. Two examples of selection rules satisfying these requirements are discussed. Uniform rates of convergence for the parameters of the infinite order VAR are also established.Very helpful comments by the editor and two referees led to a substantial improvement of the manuscript. I am particularly indebted to one of the referees for pointing out an error in the proofs. All remaining errors are my own. Financial support from NSF grant SES 0095132 is gratefully acknowledged.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 21 (2005)
Issue (Month): 01 (February)
Pages: 85-115

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Handle: RePEc:cup:etheor:v:21:y:2005:i:01:p:85-115_05

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Cited by:
  1. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation for Research in Economics, Yale University.
  2. Mayoral, Laura & Dolores Gadea, María, 2011. "Aggregate real exchange rate persistence through the lens of sectoral data," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 290-304.
  3. Laura Mayoral & Maréa Dolores Gadea, 2009. "Analyzing aggregate real exchange rate persistence through the lens of sectoral data," Working Papers 399, Barcelona Graduate School of Economics.
  4. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(04), pages 638-685, August.
  5. Theodoridis, Konstantinos, 2011. "An efficient minimum distance estimator for DSGE models," Bank of England working papers 439, Bank of England.
  6. Dietmar Bauer & Martin Wagner, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Working Papers ECO2005/09, European University Institute.
  7. Hwang, Eunju & Shin, Dong Wan, 2014. "Infinite-order, long-memory heterogeneous autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 339-358.
  8. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
  9. Laura Mayoral, 2009. "Heterogeneous dynamics, aggregation and the persistence of economic shocks," Working Papers 400, Barcelona Graduate School of Economics.
  10. Laura Mayoral, 2009. "Heterogeneous dynamics, aggregation and the persistence of economic shocks," UFAE and IAE Working Papers 786.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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