Weak Convergence of Serial Rank Statistics Under Dependence with Applications in Time Series and Markov Processes
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The Annals of Probability
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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 φ-mixing as well as strong mixing sequences of random variables. Applications in Markov processes and ARMA processes in time series are provided.
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Publisher's, offprint version
Keywords
Markov processes, Distribution functions, Topological theorems, Ergodic theory, Statistical theories, Perceptron convergence procedure, Trajectories
Citation
Puri, M. L. "Weak convergence of serial rank statistics under dependence with applications in time series and Markov processes." Annals of Probability (1990), Volume 18 Issue 3, 1361–1387. Co-author: Michel Harel.