Abstract
The local asymptotic normality property is established for a regression model with fractional ARIMA(p, d, q) errors. This result allows for solving, in an asymptotically optimal way, a variety of inference problems in the long-memory context: hypothesis testing, discriminant analysis, rankbased testing, locally asymptotically minimax and adaptive estimation, etc. The problem of testing linear constraints on the parameters, the discriminant analysis problem, and the construction of locally asymptotically minimax adaptive estimators are treated in some detail.
| Original language | English |
|---|---|
| Pages (from-to) | 2054-2080 |
| Number of pages | 27 |
| Journal | Annals of Statistics |
| Volume | 27 |
| Issue number | 6 |
| Publication status | Published - 1999 Dec |
| Externally published | Yes |
Keywords
- Adaptive estimation
- Discriminant analysis
- FARIMA model
- Local asymptotic normality
- Locally asymptotically optimal test
- Long-memory process
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty