Robust Estimation of ARMA Models with Near Root Cancellation

34 Pages Posted: 29 Jun 2013

See all articles by Timothy Cogley

Timothy Cogley

Leonard N. Stern School of Business - Department of Economics

Richard Startz

UCSB

Date Written: June 28, 2013

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 uses a simple mixture prior. The posterior 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.

Keywords: ARMA, near root cancellation, bayesian

JEL Classification: C11, C12, C22

Suggested Citation

Cogley, Timothy and Startz, Richard, Robust Estimation of ARMA Models with Near Root Cancellation (June 28, 2013). Available at SSRN: https://ssrn.com/abstract=2286799 or http://dx.doi.org/10.2139/ssrn.2286799

Timothy Cogley

Leonard N. Stern School of Business - Department of Economics ( email )

269 Mercer Street
New York, NY 10003
United States
530-752-1581 (Phone)
530-752-9382 (Fax)

Richard Startz (Contact Author)

UCSB ( email )

Department of Economics
University of California
Santa Barbara, CA 93106-9210
United States
805-893-2895 (Phone)

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