An estimator of the difference parameter in a class of long-memory time series models is examined. It is shown that, in particular circumstances, the estimator can be badly biased, and tests based on it consequently seriously misleading. The source of this bias is identified, and it is shown that its magnitude can readily be predicted through straightforward analytical arguments.
The empirical performance of tests of the Dickey-Fuller type for unit autoregressive roots in the generating model of a time series is studied. In particular, the case where the true generating model structure is unknown and may involve a substantial moving-average component is examined.
This paper develops Lagrange multiplier tests of ARMA(p, q) models against fractional ARIMA(p, d, q) alternatives. The performance of the tests is investigated for moderate-sized samples. It is concluded that fractional difference will be difficult to detect when the orders (p. q) are over-specified in an autoregressive moving-average (ARMA) analysis. The importance of distinguishing between the mean known and mean estimated cases in fractional difference models is illustrated in the context of these tests.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika.
SUMMARYThe autocorrelation function of fractional noise, when the difference parameter is positive, is quite distinctive. However, for time series of moderate length, this pattern is unlikely to be seen in the sample autocorrelations, which are severely biased when the process mean is unknown.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.