ASYMPTOTIC INFERENCE FOR NONSTATIONARY FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING-AVERAGE MODELS

Shiqing Ling and W.K. Li

Econometric Theory, 2001, vol. 17, issue 04, pages 738-764

Abstract: This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ( 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ( 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

Date: 2001
View citations in EconPapers

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466601174049 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Mike Eden ().