This paper aims at improvement in regularity conditions on spectral densities for the limit theorems of the quasi maximum-likelihood estimator and the quasi likelihood-ratio statistic. The approach parallels the Daniels-Huber-Pollard proofs of central limit theorems under nonstandard conditions for i.i.d. situations. The results of the paper enable one to dispense with excessive regularity conditions on the spectral density.
"The Bracketing Condition for Limit Theorems on Stationary Linear Processes." Ann. Statist. 17 (1) 401 - 418, March, 1989. https://doi.org/10.1214/aos/1176347024