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In-fill Asymptotic Theory for Structural Break Point in Autoregression: A Unified Theory

Author

Listed:
  • Jiang, Liang

    (School of Economics, Singapore Management University)

  • Wang, Xiaohu

    (The Chinese University of Hong Kong)

  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

This paper obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein-Uhlenbeck process when a continuous record is available. The exact distribution is asymmetric, tri-modal, dependent on the initial condition. These three properties are also found in the finite sam- ple distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models. Motivated by these observations, the paper then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient. The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers excellent approximations to the finite sample distribution. Unlike the long-span asymptotic theory, which depends on the underlying AR root and hence is tailor-made but is only available in a rather limited number of cases, the in-fill asymptotic theory is continuous in the underlying roots. Monte Carlo studies show that the in-fill asymptotic theory performs better than the long-span asymptotic theory for cases where the long-span theory is available and performs very well for cases where no long-span theory is available.

Suggested Citation

  • Jiang, Liang & Wang, Xiaohu & Yu, Jun, 2017. "In-fill Asymptotic Theory for Structural Break Point in Autoregression: A Unified Theory," Economics and Statistics Working Papers 10-2017, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2017_010
    Note: Paper available on: http://ink.library.smu.edu.sg/soe_research/1968/
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    Citations

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    Cited by:

    1. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    2. Yaein Baek, 2018. "Estimation of a Structural Break Point in Linear Regression Models," Papers 1811.03720, arXiv.org, revised Jun 2020.
    3. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    4. Andras Fulop & Jun Yu, 2017. "Bayesian Analysis of Bubbles in Asset Prices," Econometrics, MDPI, vol. 5(4), pages 1-23, October.

    More about this item

    Keywords

    Asymmetry; Bias; Exact distribution; Long-span asymptotics; In-fill asymptotics; Trimodality.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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