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Inference in heavy-tailed vector error correction models
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DOI：10.1016/j.jeconom.2019.03.008.png)
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Abstract
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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 alpha is an element of (0, 2). Furthermore, we show that the rate of convergence of the FLSE related to the short-term parameters is n(1/alpha)(L) over tilde (n) and its limiting distribution is a functional of two stable processes when alpha is an element of (1, 2), where (L) over tilde (n) is a slowly varying function. However, when alpha is an element of (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 (RISE). The results related to the short-term parameters of both ELSE and RISE 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. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Full rank LSE
Cointegration
Heavy-tailed random vector
Reduced rank LSE
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