Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes

Abstract

The asymptotic normality of linear serial rank statistics introduced by Hallin, Ingenbleek and Puri (1985) for the problem of testing white noise against ARMA alternatives is established for $\varphi$-mixing as well as strong mixing sequences of random variables. Applications in Markov processes and ARMA processes in time series are provided.