Measuring Persistence in Aggregate Output:
ARMA Models, Fractionally Integrated ARMA Models and Nonparametric Procedures

Michael A. Hauser1, Benedikt M. Pötscher2 and Erhard Reschenhofer2

1 Institut fuer Statistik, Wirtschaftsuniversität Wien, Augasse 2-6, A-1090 Vienna, Austria
2 Institut fuer Statistik und Informatik, Universität Wien, Universitätsstraße 5, A-1010 Vienna, Austria.

Preliminary version: December 1991
First version: March 1992
Second version: December 1992
Final version: December 1997


Econometric issues in the estimation of persistence in macroeconomic time series are considered. In particular, the relative merits of estimates based on ARMA models, ARFIMA models and nonparametric procedures are investigated. It is shown that ARFIMA models are inappropriate for the purpose of estimating persistence. Furthermore, some of the criticism leveled in the literature against the use of ARMA models for estimating long run properties is put into perspective. Methodological issues arising in the estimation of ARMA models that are relevant to estimation of persistence are discussed. It is shown how overparameterization of an ARMA model may lead to severely downward biased estimates of persistence. The theoretical results are employed to explain some of the findings in Campbell & Mankiw (1987a) and Christiano & Eichenbaum (1990). The methodological aspects of the paper are also relevant for the problem of estimating the value of a spectral density at any given frequency. An empirical study confirms persistence estimates reported in Campbell & Mankiw (1987a), and shows that ARMA models as well as nonparametric procedures give very similar estimates of persistence if properly applied.


We would like to thank I.R. Prucha and the participants in the Econometrics Seminar at the Institute for Advanced Studies Vienna for helpful comments on an earlier version of the paper. An earlier version of this paper was also presented at the 1992 Econometric Society European Meeting.

JEL classification: C22, E32

Key Words: ARMA model, fractionally integrated ARMA model, persistence, spectral density estimation