We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616–621] and motivated by Gordin [Soviet Math. Dokl. 10 (1969) 1174–1176]. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.
Magda Peligrad. Sergey Utev. "Central limit theorem for stationary linear processes." Ann. Probab. 34 (4) 1608 - 1622, July 2006. https://doi.org/10.1214/009117906000000179