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Abstract: This paper studies the residual empirical process of long- and short-memorytime series regression models and establishes its uniform expansion under ageneral framework. The results are applied to the stochastic regression modelsand unstable autoregressive models. For the long-memory noise, it is shown thatthe limit distribution of the Kolmogorov-Smirnov test statistic studied in Hoand Hsing Ann. Statist. 24 1996 992-1024 does not hold when the stochasticregression model includes an unknown intercept or when the characteristicpolynomial of the unstable autoregressive model has a unit root. To this end,two new statistics are proposed to test for the distribution of the long-memorynoises of stochastic regression models and unstable autoregressive models.With Correction.



Author: Ngai Hang Chan, Shiqing Ling

Source: https://arxiv.org/







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