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On linear processes with dependent innovations

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  • Biao Wu, Wei
  • Min, Wanli

Abstract

We consider asymptotic behavior of partial sums and sample covariances for linear processes whose innovations are dependent. Central limit theorems and invariance principles are established under fairly mild conditions. Our results go beyond earlier ones by allowing a quite wide class of innovations which includes many important nonlinear time series models. Applications to linear processes with GARCH innovations and other nonlinear time series models are discussed.

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  • Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:6:p:939-958
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    6. Paparoditis, Efstathios & Politis, Dimitris N, 2013. "The Asymptotic Size and Power of the Augmented Dickey-Fuller Test for a Unit Root," University of California at San Diego, Economics Working Paper Series qt0784p55m, Department of Economics, UC San Diego.
    7. Jirak, Moritz, 2011. "On the maximum of covariance estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1032-1046, July.
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    9. Zhengyan Lin & Hanchao Wang, 2016. "On Convergence to Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 29(3), pages 717-736, September.
    10. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    11. Zhang, Rong-Mao & Sin, Chor-yiu (CY) & Ling, Shiqing, 2015. "On functional limits of short- and long-memory linear processes with GARCH(1,1) noises," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 482-512.
    12. Jérôme Dedecker & Florence Merlevède & Dalibor Volný, 2007. "On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 20(4), pages 971-1004, December.
    13. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    14. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
    15. Stefan Richter & Weining Wang & Wei Biao Wu, 2018. "A supreme test for periodic explosive GARCH," Papers 1812.03475, arXiv.org.
    16. Florence Merlevède & Magda Peligrad, 2010. "Moderate Deviations for Linear Processes Generated by Martingale-Like Random Variables," Journal of Theoretical Probability, Springer, vol. 23(1), pages 277-300, March.
    17. Hui, Yongchang & Wong, Wing-Keung & Bai, Zhidong & Zhu, Zhenzhen, 2016. "A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications," MPRA Paper 75216, University Library of Munich, Germany.
    18. Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.
    19. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 892-908, November.
    20. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.
    21. Steland, Ansgar & von Sachs, Rainer, 2016. "Asymptotics for High–Dimensional Covariance Matrices and Quadratic Forms with Applications to the Trace Functional and Shrinkage," LIDAM Discussion Papers ISBA 2016038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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