Abstract: This paper establishes central limit theorems and invariance principles for functionals of one-sided linear processes. These results are applied to long-range dependent sequences whose covariances are summable but not absolutely summable. We also consider empirical processes and 0-crossings for linear processes whose innovations may have infinite variance. Comparisons with earlier results are indicated.
Key words and phrases: Central limit theorem, invariance principle, long- and short-range dependence, linear process, 0-crossings, empirical process, martingale.