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Robust Estimation of ARMA Models with Near Root Cancellation

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  • Cogley, Timothy
  • Startz, Richard

Abstract

Standard estimation of ARMA models in which the AR and MA roots nearly cancel, so that individual coefficients are only weakly identified, often produces inferential ranges for individual coefficients that give a spurious appearance of accuracy. We remedy this problem with a model that mixes inferential ranges from the estimated model with those of a more parsimonious model. The mixing probability is derived using Bayesian methods, but we show that the method works well in both Bayesian and frequentist setups. In particular, we show that our mixture procedure weights standard results heavily when given data from a well-identified ARMA model (which does not exhibit near root cancellation) and weights heavily an uninformative inferential region when given data from a weakly-identified ARMA model (with near root cancellation). When our procedure is applied to a well-identified process the investigator gets the “usual results,†so there is no important statistical cost to using our procedure. On the other hand, when our procedure is applied to a weakly-identified process, the investigator learns that the data tell us little about the parameters—and is thus protected against making spurious inferences. We recommend that mixture models be computed routinely when inference about ARMA coefficients is of interest.

Suggested Citation

  • Cogley, Timothy & Startz, Richard, 2012. "Robust Estimation of ARMA Models with Near Root Cancellation," University of California at Santa Barbara, Economics Working Paper Series qt0cw056qz, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbec:qt0cw056qz
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    References listed on IDEAS

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    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. Nelson, Charles R. & Startz, Richard, 2007. "The zero-information-limit condition and spurious inference in weakly identified models," Journal of Econometrics, Elsevier, vol. 138(1), pages 47-62, May.
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    Keywords

    Social and Behavioral Sciences; ARMA; bayesian; weak identification;

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