Central limit theorem for stationary linear processes. (English) Zbl 1101.60014

Peligrad, Magda; Utev, Sergey

Ann. Probab. 34, No. 4, 1608-1622 (2006).

Summary: We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined by D. L. McLeish [Ann. Probab. 5, 616–621 (1977; Zbl 0367.60021)] and motivated by M. I. Gordin [Sov. Math., Dokl. 10, 1174–1176 (1969); translation from Dokl. Akad. Nauk SSSR 188, 739–741 (1969; Zbl 0212.50005)]. 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.

MSC:

60F05	Central limit and other weak theorems
60G10	Stationary stochastic processes
60G42	Martingales with discrete parameter
60G48	Generalizations of martingales

Keywords:

ergodic theorem; martingale

Citations:

Zbl 0367.60021; Zbl 0212.50005

References:

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