Abstract
This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent
to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and
quite general and, in particular, encompasses the multivariate non-cointegrated fractional autoregressive integrated moving
average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and
to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in
probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where
uniform convergence fails is handled using a truncation argument
to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and
quite general and, in particular, encompasses the multivariate non-cointegrated fractional autoregressive integrated moving
average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and
to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in
probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where
uniform convergence fails is handled using a truncation argument
| Original language | English |
|---|---|
| Journal | Journal of Time Series Analysis |
| Volume | 36 |
| Issue | 2 |
| Pages (from-to) | 154–188 |
| ISSN | 0143-9782 |
| DOIs | |
| Publication status | Published - 2015 |