Measuring Persistence in Aggregate Output:
ARMA Models, Fractionally Integrated ARMA Models and Nonparametric Procedures
Michael A. Hauser1,
Benedikt M. Pötscher2 and Erhard Reschenhofer2
Institut fuer Statistik, Wirtschaftsuniversität Wien, Augasse 2-6, A-1090
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.
ARMA model, fractionally integrated ARMA model, persistence, spectral density estimation