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Residual Log-Periodogram Inference for Long-Run-Relationships

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  • Hassler, Uwe
  • Marmol, Francesc
  • Velasco, Carlos

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.

Suggested Citation

  • Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2009. "Residual Log-Periodogram Inference for Long-Run-Relationships," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 77562, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    • Handle: RePEc:dar:wpaper:77562
    Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/77562/
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    References listed on IDEAS

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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