Local asymptotic normality for regression models with long-memory disturbance
The authors derive asymptotic theory based on a local asymptotic normality (LAN) approach for a regression model with stationary non-Gaussian fractional ARIMA\((p,d,q)\) long-memory errors. It is shown that the log-likelihood ratios have the typical LAN behavior and thus the local experiments converge weakly to a Gaussian shift experiment. The results are applied to testing linear constraints on the parameters, discriminant analysis, construction of locally asymptotically minimax adaptive estimators, and other inference problems. A general formula for the distribution, under contiguous sequences of alternatives, for a class of statistics is established. The results are valid under a very large family of innovation densities.
scientific article; zbMATH DE number 1523486