Empirical processes for infinite variance autoregressive models
The paper proposes new procedures for diagnostic checking of fitted models under the assumption of infinite-variance errors which are in the domain of attraction of a stable law. These procedures are functional of residual-based empirical processes. First, the asymptotic distributions of the empirical processes based on residuals are derived. Then two important applications in time series diagnostics are discussed. A goodness-of-fit test is developed using a functional of the empirical process based on residuals. Tests of independence of innovations are also considered. The finite-sample behavior of these tests are studied by simulation and comparison with the classical Portmanteau tests for ARMA models with infinite-variance developed recently by Lin and McLeod (2008)  is provided.
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Volume (Year): 107 (2012)
Issue (Month): C ()
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- J.-W. Lin & A. I. McLeod, 2008. "Portmanteau tests for ARMA models with infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 600-617, 05.
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- Lee, Sangyeol, 1997. "A note on the residual empirical process in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 405-411, April.
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- Caner, Mehmet, 1998. "Tests for cointegration with infinite variance errors," Journal of Econometrics, Elsevier, vol. 86(1), pages 155-175, June.
- Jiazhu Pan & Hui Wang & Qiwei Yao, 2007. "Weighted least absolute deviations estimation for ARMA models with infinite variance," LSE Research Online Documents on Economics 5405, London School of Economics and Political Science, LSE Library.
- Davis, Richard A., 1996. "Gauss-Newton and M-estimation for ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 75-95, October.
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