Inference in heavy-tailed vector error correction models

She, Rui; Ling, Shiqing

doi:10.1016/j.jeconom.2019.03.008

Cited by 8 publications

(20 citation statements)

References 29 publications

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“…By Theorem A.1 and Lemma B.1 in She and Ling (2020), it is straightforward to show the following lemma.…”

Section: Appendixmentioning

confidence: 92%

“…Caner (1998) developed the asymptotic theory for residual-based tests and quasi-likelihood ratio tests for cointegration under the assumption of infinite variance errors. She and Ling (2020) studied the heavy-tailed VEC model and established the asymptotic theory of the full rank LSE (FLSE) and reduced rank LSE (RLSE). However, this theory cannot be applied for testing the cointegrating rank of the heavy-tailed VEC model.…”

Section: Introductionmentioning

confidence: 99%

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Automated Estimation of Heavy-Tailed Vector Error Correction Models

Guo¹,

Ling²,

Mi³

2023

STAT SINICA

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This paper proposes an automated approach via adaptive shrinkage techniques to determine the co-integrating rank and estimate parameters simultaneously in the VEC model with unknown order p when its noises are i.i.d. heavy-tailed random vectors with tail index α ∈ (0, 2). It is showed that the estimated co-integrating rank and order p equal to the true rank and the true order p0, respectively, with probability trending to 1 as the sample size n → ∞, while other estimated parameters achieve the oracle property, that is, they have the same rate of convergence and the same limiting distribution as those of estimated parameters when the co-integrating rank and the true order p0 are known. This paper also proposes a data-driven procedure of selecting the tuning parameters.Simulation studies are carried to evaluate the performance of this procedure in finite samples. Our techniques are applied to explore the long-run and short-run behavior of prices of wheat, corn and wheat in USA.

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“…By Theorem A.1 and Lemma B.1 in She and Ling (2020), it is straightforward to show the following lemma.…”

Section: Appendixmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Automated Estimation of Heavy-Tailed Vector Error Correction Models

Guo¹,

Ling²,

Mi³

2023

STAT SINICA

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“…The case m = 0 correspond to y t being (asymptotically) strictly stationary. Assumption 1 is also implied by Assumption 2.1 in She and Ling (2020), where a finiteorder VAR model under the classic I (1) conditions stated e.g. in Ahn and Reinsel (1990) is considered.…”

Section: Theorymentioning

confidence: 99%

“…Caner (1998) derives the asymptotic distribution of Johansen's trace test under infinite variance and shows that it depends on the (unknown) tail index of the data. She and Ling (2020) study the (non-standard) rate of convergence of estimators in non-stationary VAR models and show that the limiting distributions depend on the tail index in a non-trivial fashion; similar results are also found in Paulauskas and Rachev (1998) and Fasen (2013). In the univariate case, Jach and Kokoszka (2004) and show that suitable (respectively, M-out-of-N and wild) bootstrap approaches could be used to test whether data are driven by a stochastic trend; knowledge of the tail index is not needed, but extensions of these bootstrap approaches to multiple time series are not available, and are likely to be extremely difficult to develop and implement.…”

Section: Introductionmentioning

confidence: 99%

Inference in heavy-tailed non-stationary multivariate time series

Barigozzi¹,

Cavaliere²,

Trapani³

2021

Preprint

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We study inference on the common stochastic trends in a non-stationary, N -variate time series y t , in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail index, or even knowledge as to whether certain moments (such as the variance) exist or not, and develop an estimator of the number of stochastic trends m based on the eigenvalues of the sample second moment matrix of y t . We study the rates of such eigenvalues, showing that the first m ones diverge, as the sample size T passes to infinity, at a rate faster by O (T ) than the remaining N − m ones, irrespective of the tail index. We thus exploit this eigen-gap by constructing, for each eigenvalue, a test statistic which diverges to positive infinity or drifts to zero according to whether the relevant eigenvalue belongs to the set of the first m eigenvalues or not. We then construct a randomised statistic based on this, using it as part of a sequential testing procedure, ensuring consistency of the resulting estimator of m. We also discuss an estimator of the common trends based on principal components and show that, up to a an invertible linear transformation, such estimator is consistent in the sense that the estimation error is of smaller order than the trend itself. Finally, we also consider the case in which we relax the standard assumption of i.i.d. innovations, by allowing for heterogeneity of a very general form in the scale of the innovations. A Monte Carlo study shows that the proposed estimator for m performs particularly well, even in samples of small size. We complete the paper by presenting four illustrative applications covering commodity prices, interest rates data, long run PPP and cryptocurrency markets.

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“…Koedijk and Kool (1992) studied the exchange rate returns for three East European currencies and found that their tail indices are smaller than 2. Francq and Zakoïan (2013) investigated nine major financial markets in the world and argued that the time series modelling driven by a heavy-tailed noise may be more appropriate to financial data analysis; see Rachev (2003) and She and Ling (2020), among many others. All previous evidences show that there is a practical and urgent need to study the heavy-tailed time series.…”

Section: Introductionmentioning

confidence: 99%

Tests of Unit Root Hypothesis With Heavy-Tailed Heteroscedastic Noises

She¹

2023

STAT SINICA

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This paper studies the unit-root testing with unspecified and heavy-tailed heteroscedastic noises. A new weighted least squares estimation (WLSE) is designed to be used in the Dickey-Fuller (DF) test, of which the asymptotic normality is verified. However, the performance of the DF test strongly relies on the estimation accuracy of the asymptotic variance, which is not stable for dependent time series. To overcome this issue, we develop two novel unit-root tests by applying the empirical likelihood technique to the WLSE score equation. It is shown that both of the empirical likelihood-based tests converge weakly to a chi-squared distribution with one degree of freedom. Furthermore, the limiting theory is extended to the weighted M -estimation score equation. In contrast to existing unit-root tests for heavy-tailed time series, the empirical likelihood tests do not involve any estimators of the unknown parameters or any restrictions on the tail index of noise, which is of more practical appealing, and thus can be widely used in finance and econometrics. Extensive simulation studies are conducted to examine the effectiveness of the proposed methods.

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Inference in heavy-tailed vector error correction models

Cited by 8 publications

References 29 publications

Automated Estimation of Heavy-Tailed Vector Error Correction Models

Automated Estimation of Heavy-Tailed Vector Error Correction Models

Inference in heavy-tailed non-stationary multivariate time series

Tests of Unit Root Hypothesis With Heavy-Tailed Heteroscedastic Noises

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