High-dimensional time series may well be the most common type of dataset in the so-called “big data” revolution, and have entered current practice in many areas, including meteorology, genomics, chemometrics, connectomics, complex physics simulations, biological and environmental research,...

We consider the class of simple random walks or birth and death chains on the nonnegative integers. The set of return probabilities Pn00, n [greater-or-equal, slanted] 0, uniquely determines the spectral measure of the process. We characterize the class of simple random walks with the same...

In a recent paper, Mokkadem (1997. Stoch. Proc. Appl. 72, 145-149) derived a simple test for randomness against ARMA alternatives. In this note we consider a transformation of the corresponding statistic and present an alternative proof of this result. Through this approach it is demonstrated...