In this paper we study the relationship between the number of replications and the accuracy of the estimated quantiles of a distribution obtained by simulation. A method for testing hypotheses on the quantiles of a theoretical distribution using the simulated distribution is proposed, as well as a method to check the hypothesis of consistency of a test.Financial support from research projects PB96-1469-C05-01, UPV-038.321-G55/98 and PI9970 is gratefully acknowledged.

This note discusses the concept of aliasing and its use in the paper by H.J. Bierens (2001, Econometric Theory 17, 962–983), in the framework of a second-order autoregression with complex unit roots. The condition on the range of the angular frequency φ is extended to φ ∈ (0,2π) − {π}.Financial support from UPV-EHU research project 9/UPV-00038.321-13503/2001, Basque Government project PI9970 and Ministerio de ciencia y tecnología BEC2003-02028 is gratefully acknowledged.

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When working with time series data observed at intervals smaller than a year, it is often necessary to test for the presence of seasonal unit roots.One of the most widely used methods for testing seasonal unit roots is that of HEGY, which provides test statistics with non-standard distributions. This paper describes a generalisation of this method for any periodicity and uses a response surface regressions approach to calculate the critical values and P values of the HEGY statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and some new tables of critical values for daily, hourly and halfhourly data are presented.