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Martingale decomposition and approximations for nonlinearly dependent processes

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  • Lee, Ji Hyung

Abstract

This paper proposes a new martingale (MG) decomposition (Gordin, 1969; Hall and Heyde, 1980) for a dependent time series under a predictive dependence measure based on Wu (2005). The decomposition produces a generalized version of the Beveridge–Nelson (BN) lemma (Phillips and Solo, 1992) that accommodates many nonlinear time series, such as GARCH models and threshold autoregressive processes, thereby extending the empirical ambit of the original lemma designed for the linear process. Under this extended framework, MG approximations can be constructed for weighted sums of the nonlinear dependent processes and these approximations lead directly to a new central limit theorem whose range of application includes many practical time series models.

Suggested Citation

  • Lee, Ji Hyung, 2019. "Martingale decomposition and approximations for nonlinearly dependent processes," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 35-42.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:35-42
    DOI: 10.1016/j.spl.2019.04.012
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    1. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    4. Wu, Wei Biao, 2006. "Unit Root Testing For Functionals Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 22(1), pages 1-14, February.
    5. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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