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Latent Local-to-Unity Models

Author

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  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

This paper proposes a class of state-space models where the state equation is a local-to-unity process. The large sample theory is obtained for the least squares (LS) estimator of the autoregressive (AR) parameter in the AR representation of the model under two sets of conditions. In the first set of conditions, the error term in the observation equation is independent and identically distributed (iid), and the error term in the state equation is stationary and fractionally integrated with memory parameter H ϵ 2 (0; 1). It is shown that both the rate of convergence and the asymptotic distribution of the LS estimator depend on H. In the second set of conditions, the error term in the observation equation is independent but not necessarily identically distributed, and the error term in the state equation is strong mixing. When both error terms are iid, we also develop the asymptotic theory for an instrumental variable estimator. Special cases of our models are discussed.

Suggested Citation

  • Yu, Jun, 2021. "Latent Local-to-Unity Models," Economics and Statistics Working Papers 4-2021, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2021_004
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    Cited by:

    1. Shuping Shi & Jun Yu, 2023. "Volatility Puzzle: Long Memory or Antipersistency," Management Science, INFORMS, vol. 69(7), pages 3861-3883, July.

    More about this item

    Keywords

    State-space; Local-to-unity; O-U process; Fractional O-U process; Fractional Brownian motion; Fractional integration; Instrumental variable;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G01 - Financial Economics - - General - - - Financial Crises

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