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Residual Log-Periodogram Inference for Long-Run-Relationships

Hassler, Uwe and Marmol, Francesc and Velasco, Carlos (2002):
Residual Log-Periodogram Inference for Long-Run-Relationships.
Darmstadt, In: Darmstadt Discussion Papers in Economics, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/4814],
[Report]

Abstract

We assume that some consistent estimator of an equilibrium relation between non-stationary fractionally integrated series is used in a first step to compute residuals (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate and test the degree of persistence of the equilibrium deviation. Provided the first step estimator converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of persistence from residuals. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on the persistence. Our assumptions allow for stationary deviations with long memory as well as for non-stationary but transitory equilibrium errors. In particular, in case of several regressors we consider the joint estimation of the memory parameters of the observed series and of the equilibrium deviation. Wald statistics to test for parameter restrictions of the system have a limiting chi-squared distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics.

Item Type: Report
Erschienen: 2002
Creators: Hassler, Uwe and Marmol, Francesc and Velasco, Carlos
Title: Residual Log-Periodogram Inference for Long-Run-Relationships
Language: English
Abstract:

We assume that some consistent estimator of an equilibrium relation between non-stationary fractionally integrated series is used in a first step to compute residuals (or differences thereof). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate and test the degree of persistence of the equilibrium deviation. Provided the first step estimator converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of persistence from residuals. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on the persistence. Our assumptions allow for stationary deviations with long memory as well as for non-stationary but transitory equilibrium errors. In particular, in case of several regressors we consider the joint estimation of the memory parameters of the observed series and of the equilibrium deviation. Wald statistics to test for parameter restrictions of the system have a limiting chi-squared distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics.

Series Name: Darmstadt Discussion Papers in Economics
Volume: 115
Place of Publication: Darmstadt
Uncontrolled Keywords: Fractional cointegration; semiparametric inference; limiting normality; long memory; non-stationarity; exchange rates.
Divisions: 01 Department of Law and Economics
01 Department of Law and Economics > Volkswirtschaftliche Fachgebiete
Date Deposited: 07 Feb 2016 20:55
Official URL: http://tuprints.ulb.tu-darmstadt.de/4814
URN: urn:nbn:de:tuda-tuprints-48149
Additional Information:

JEL Classification: C14, C22

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