Time-Varying Cointegration

Bierens, Herman J.; Martins, Luís F.

doi:10.1017/s0266466609990648

Cited by 151 publications

(186 citation statements)

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“…The Chebyshev polynomials used by Bierens (1997), Bierens and Martins (2010), and in the present paper, are the ones of the "first kind." They are a special case of the Gegenbauer polynomials.…”

Section: Appendixmentioning

confidence: 90%

“…Hence, within the analysis of the order of integration of the variables, Bierens (1997) unit root tests, allow us to test whether the process is linear or non-linear trend stationary. In addition Bierens and Martins (2010) propose the use of Chebyshev polynomials in the framework of time-varying cointegrating parameters. There are several advantages in using these polynomials; first, since they are orthogonal, it avoids the problem of near collinearity in the regressors matrix in comparison with using regular time polynomials.…”

Section: The Statistical Modelmentioning

confidence: 99%

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Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Cuestas

Gil-Alana

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

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This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev's polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article.

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Section: Appendixmentioning

confidence: 90%

Section: The Statistical Modelmentioning

confidence: 99%

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Cuestas

Gil-Alana

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

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“…This would be possible by using the timevarying VECM framework, by Bierens and Martins (2010), which is an extension of the methods proposed by Johansen (1988Johansen ( , 1991Johansen ( , 1995 and allows to analyze the development of the cointegration relationship over time. Another promising approach in this research area might be using a Bayesian framework, for example Koop et al (2011) also offer the possibility to explicitly allow the cointegration space to evolve over time.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Do They Still Matter? – Impact of Fossil Fuels on Electricity Prices in the Light of Increased Renewable Generation

Lips

2017

Journal of Time Series Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractDuring the last years, the German energy sector and especially its electricity market was affected by a major energy transition, the so called "Energiewende". This transition led to an increase of electricity production from renewable sources and thereby affected the whole electricity market. Therefore, it provides lessons for countries, which are only beginning a similar transition away from fossil fuels to renewable energy sources. The aim of this analysis is to assess if there still exists a relationship between fossil fuel and electricity prices. Due to possible structural breaks in the time series a minimum Lagrange Multiplier (LM) stationarity test is applied, which endogenously determines possible structural breaks. Subsequently a bootstrap approach is used to estimate confidence intervals (C.I.s) for the test statistic and the possible break dates. Furthermore, the stability of the cointegration vector is assessed with the test by Hansen and Johansen (1999). The results indicate that the cointegration relationship is not stable over time. To incorporate these findings, the cointegration analysis is based on Johansen et al. (2000), which allows structural breaks in the deterministic part of the cointegration relation. These results supports the assumption that the energy transition affected the relationship between fossil fuels and electricity prices, although there still exists a relatively strong cointegration relation between fossil fuel and electricity prices in the long run.Keywords: Structural Breaks, Bootstrap, Stationarity Test, Cointegration, Energy Economics, German Energy Transition JEL classification: C58, G14, L94, Q41. * I am grateful to Peter Winker, all my colleagues and the participants of the MAGKS Colloquium (Marburg) for helpful comments and fruitful discussions.

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“…if fu t g is I(0)), we also employ "standard" tests with the null hypothesis of no cointegration (ADF, Z and Z t tests) 7 , as well as their counterparts that allow for regime shifts, developed by Gregory and Hansen (1996), in which the cointegrating vector may be subject to a regime shift at an unknown time under the alternative hypothesis. 8 In this framework, since the change point or its occurrence are unknown, the testing procedures involve computing the usual statistics (GH-AEG, GH-Z t and GH-Z ) for all possible break points and then selecting the smallest value obtained, since it will potentially present greater evidence against the null hypothesis of no cointegration.…”

Section: Preliminary Analysismentioning

confidence: 99%

“…The same applies to structural change tests used as cointegration tests. 7 To choose an appropriate lag length for the ADF test, we adopt a downward testing selection procedure based on two-sided 5%-level t-type tests for the signi…cance of the coe¢ cient on the longest lag, with the maximum lag length set equal to 8. For the Z and Zt tests, the long-run variance of f t g is estimated by using a prewhitened quadratic spectral kernel estimator with a data-based bandwidth and a …rst-order autoregressive prewhitening …lter, as recommended in Andrews and Monahan (1992).…”

Section: Preliminary Analysismentioning

confidence: 99%