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A Simple Test Of Normality For Time Series

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  • Lobato, Ignacio N.
  • Velasco, Carlos

Abstract

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its simplicity, because it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.We are very grateful to Don Andrews and two referees for useful comments and suggestions. We are especially thankful to a referee who provided a FORTRAN code. Lobato acknowledges financial support from Asociación Mexicana de Cultura and from Consejo Nacional de Ciencia y Tecnologìa (CONACYT) under project grant 41893-S. Velasco acknowledges financial support from Spanish Dirección General de Enseñanza Superior, BEC 2001-1270.

Suggested Citation

  • Lobato, Ignacio N. & Velasco, Carlos, 2004. "A Simple Test Of Normality For Time Series," Econometric Theory, Cambridge University Press, vol. 20(4), pages 671-689, August.
    • Handle: RePEc:cup:etheor:v:20:y:2004:i:04:p:671-689_20
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    1. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    2. Antonio Aguirre & Ignacio N. Lobato, 2024. "Evidence of non-fundamentalness in OECD capital stocks," Empirical Economics, Springer, vol. 67(2), pages 761-772, August.
    3. G. Kontogeorgos & K. Lambrias, 2022. "Evaluating the Eurosystem/ECB staff macroeconomic projections: The first 20 years," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 213-229, March.
    4. Fausto Hern'andez Trillo & C. Vladimir Rodr'iguez-Caballero & Daniel Ventosa-Santaul`aria, 2024. "Monopoly Unveiled: Telecom Breakups in the US and Mexico," Papers 2407.09695, arXiv.org.
    5. Mohamed Boutahar, 2010. "Behaviour of skewness, kurtosis and normality tests in long memory data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 193-215, June.
    6. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    7. Zacharias Psaradakis & Marián Vávra, 2017. "Normality Tests for Dependent Data: Large-Sample and Bootstrap Approaches," Birkbeck Working Papers in Economics and Finance 1706, Birkbeck, Department of Economics, Mathematics & Statistics.
    8. Donghang Luo & Ke Zhu & Huan Gong & Dong Li, 2020. "Testing error distribution by kernelized Stein discrepancy in multivariate time series models," Papers 2008.00747, arXiv.org.
    9. Kontogeorgos, Georgios & Lambrias, Kyriacos, 2019. "An analysis of the Eurosystem/ECB projections," Working Paper Series 2291, European Central Bank.
    10. Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    11. Solomon Temidayo Owolabi & Kakaba Madi & Ahmed Mukalazi Kalumba, 2021. "Comparative evaluation of spatio-temporal attributes of precipitation and streamflow in Buffalo and Tyume Catchments, Eastern Cape, South Africa," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(3), pages 4236-4251, March.
    12. Psaradakis, Zacharias & Vávra, Marián, 2017. "A distance test of normality for a wide class of stationary processes," Econometrics and Statistics, Elsevier, vol. 2(C), pages 50-60.
    13. Chen, Yi-Ting, 2012. "A simple approach to standardized-residuals-based higher-moment tests," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 427-453.
    14. Jara, Alejandro & Piña, Marco, 2023. "Exchange rate volatility and the effectiveness of FX interventions: The case of Chile," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(2).
    15. Chioneso S. Marange & Yongsong Qin & Raymond T. Chiruka & Jesca M. Batidzirai, 2023. "A Blockwise Empirical Likelihood Test for Gaussianity in Stationary Autoregressive Processes," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    16. Malahayati, Marissa, 2023. "Indonesia’s forest management progress: empirical analysis of environmental Kuznets curve," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 9(3), September.
    17. Marian Vavra, 2016. "Testing the Validity of Assumptions of UC-ARIMA Models for Trend-Cycle Decompositions," Working and Discussion Papers WP 4/2016, Research Department, National Bank of Slovakia.
    18. Alegría, Alfredo & Emery, Xavier, 2024. "Matrix-valued isotropic covariance functions with local extrema," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    19. Nieto-Reyes, Alicia & Cuesta-Albertos, Juan Antonio & Gamboa, Fabrice, 2014. "A random-projection based test of Gaussianity for stationary processes," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.

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