Abstract
This paper is concerned with statistical inference of nonstationary and non-invertible autoregressive moving-average (ARMA) processes. It makes use of the fact that a derived process of an ARMA(p, q) model follows an AR(q) model with an autoregressive (AR) operator equivalent to the moving-average (MA) part of the original ARMA model. Asymptotic distributions of least squares estimates of MA parameters based on a constructed derived process are obtained as corresponding analogs of a nonstationary AR process. Extensions to the nearly non-invertible models are considered and the limiting distributions are obtained as functionals of stochastic integrals of Brownian motions and Ornstein-Uhlenbeck processes. For application, a two-stage procedure is proposed for testing unit roots in the MA polynomial. Examples are given to illustrate the application.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Journal | Journal of Time Series Analysis |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 1996 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- Brownian motions
- Derived processes
- Difference-stationarity
- Least squares
- Near non-invertibility
- Nonstationarity
- Ornstein-Uhlenbeck processes
- Stochastic integrals
- Trend-stationarity
Policy Impact
- Cited in Policy Documents
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