We suggest a convenient version of the omnibus test for normality, using skewness and kurtosis based on Shenton and Bowman [Journal of the American Statistical Association (1977) Vol. 72, pp. 206-211], which controls well for size, for samples as low as 10 observations. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The first power experiments consider the whole skewness-kurtosis plane; the second use a bivariate distribution which has normal marginals. It is concluded that the proposed test has the best size and power properties of the tests considered.

Statistical Algorithms for Models in State Space Using SsfPack 2.2Koopman, S.J.M.; Shephard, N.; Doornik, J.A. Publication date: 1998Link to publication Citation for published version (APA):Koopman, S. J. M., Shephard, N., & Doornik, J. A. (1998). Statistical Algorithms for Models in State Space Using SsfPack 2.2. (CentER Discussion Paper; Vol. 1998-141). Tilburg: Econometrics. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we h a v e made to the Ox computing environment. SsfPack allows for a full range of di erent state space forms: from a simple time-invariant model to a complicated time-varying model. Functions can be used which put standard models such as ARIMA and cubic spline models in state space form. Basic functions are available for ltering, moment smoothing and simulation smoothing. Ready-to-use functions are provided for standard tasks such as likelihood evaluation, forecasting and signal extraction. We show that SsfPack can be easily used for implementing, tting and analysing Gaussian models relevant t o many areas of econometrics and statistics. Some Gaussian illustrations are given.

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The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accurate than the standard tables previously published.

The paper addresses the practical determination of cointegration rank. This is difficult for many reasons: deterministic terms play a crucial role in limiting distributions, and systems may not be formulated to ensure similarity to nuisance parameters; finite-sample critical values may differ from asymptotic equivalents; dummy variables alter critical values, often greatly; multiple cointegration vectors must be identified to allow inference; the data may be I(2) rather than I(1), altering distributions; and conditioning must be done with care. These issues are illustrated by an empirical application of multivariate cointegration analysis to a small model of narrow money, prices, output and interest rates in the UK.