Herein we obtain several almost sure and Lp convergence properties of generalized linear processes. When the generalized linear process is generated by an orthonormal Sp system (which includes the classical i.i.d. white noise, Lp bounded martingale difference sequences and weakly multiplicative...

Multivariate self-normalized processes, for which self-normalization consists of multiplying by the inverse of a positive definite matrix (instead of dividing by a positive random variable as in the scalar case), are ubiquitous in statistical applications. In this paper we make use of a...