On large deviations in the Gaussian autoregressive process: stable, unstable and explosive cases
Bercu, Bernard
Bernoulli, Tome 7 (2001) no. 6, p. 299-316 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For the Gaussian autoregressive process, the asymptotic behaviour of the Yule-Walker estimator is totally different in the stable, unstable and explosive cases. We show that, irrespective of this trichotomy, this estimator shares quite similar large deviation properties in the three situations. However, in the explosive case, we obtain an unusual rate function with a discontinuity point at its minimum.
Publié le : 2001-04-14
Classification:  autoregressive Gaussian process,  estimation,  large deviations 
@article{1080222089,
     author = {Bercu, Bernard},
     title = {On large deviations in the Gaussian autoregressive process: stable, unstable and explosive cases},
     journal = {Bernoulli},
     volume = {7},
     number = {6},
     year = {2001},
     pages = { 299-316},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1080222089}
}

Bercu, Bernard. On large deviations in the Gaussian autoregressive process: stable, unstable and explosive cases. Bernoulli, Tome 7 (2001) no. 6, pp.  299-316. http://gdmltest.u-ga.fr/item/1080222089/