The authors propose a nonparametric test for white noise hypothesis in a regression model. The test is based on a regressogram estimate, which bin width is selected using a penalty method similar to the AIC, BIC, and C'ps MAllows criteria.

We prove in this paper the validity of an Edgeworth expansion to the joint distribution of the sample autocorrelations of a stationary, Gaussian, long memory process. The method of proof relies of Durbin's (1980\) suitably modified conditions for the validity of a multivariate Edgeworth expansion.

The ARFIMA model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there has been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood...

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers many types of ARFIMA models.

We derive asymptotic properties of estimators and test statistics to determine—in a grouped data setting—common versus group‐specific factors. Despite the fact that our test statistic for the number of common factors, under the null, involves a parameter at the boundary (related to unit...