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Inference in heavy-tailed vector error correction models

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  • She, Rui
  • Ling, Shiqing

Abstract

This paper first studies the full rank least squares estimator (FLSE) of the heavy-tailed vector error correction (VEC) models. It is shown that the rate of convergence of the FLSE related to the long-run parameters is n (sample size) and its limiting distribution is a stochastic integral in terms of two stable random processes when the tail index α∈(0,2). Furthermore, we show that the rate of convergence of the FLSE related to the short-term parameters is n1∕αL̃(n) and its limiting distribution is a functional of two stable processes when α∈(1,2), where L̃(n) is a slowly varying function. However, when α∈(0,1), we show that the rate of convergence of the FLSE related to the short-term parameters is n and its limiting distribution not only depends on the stationary component itself but also depends on the unit root component. Based on the FLSE, we then study the limiting behavior of the reduced rank LSE (RLSE). The results related to the short-term parameters of both FLSE and RLSE are significantly different from those of heavy-tailed time series in the literature, and it may provide new insights in the area for future research. Simulation study is carried out to demonstrate the performance of both estimators. A real example with application to 3-month Treasury Bill rate, 1-year Treasury Bill rate and Federal Fund rate is given.

Suggested Citation

  • She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
  • Handle: RePEc:eee:econom:v:214:y:2020:i:2:p:433-450
    DOI: 10.1016/j.jeconom.2019.03.008
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    Cited by:

    1. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    2. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

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    More about this item

    Keywords

    Full rank LSE; Cointegration; Heavy-tailed random vector; Reduced rank LSE;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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