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Contributions to Risk Assessment with Edgeworth–Sargan Density Expansions (I): Stability Testing

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  • Ignacio Mauleón

    (Department of Economics & Business, Universidad Rey Juan Carlos, 28032 Madrid, Spain)

Abstract

This paper analytically derives a stability test for the probability distribution of a random variable that follows the Edgeworth–Sargan density, also called Gram–Charlier. The distribution of the test is a weighted sum of Chi-squared densities of increasing degrees of freedom, starting with the standard equivalent Chi-squared under the same conditions. The weights turn out to be linear combinations of the parameters of the distribution and the moments of a Gaussian density, and can be computed exactly. This is a convenient result, since then the probability intervals can be easily calculated from existing Chi-squared distribution tables. The test is applied to assess the weekly solar irradiance data stability for a twelve-year period. It shows that the density is acceptably stable overall, except for some eventual and localised dates. It is also shown that the usual probability intervals implemented in stability testing are larger than those of the equivalent Chi-squared distribution under comparable conditions. This implies that the common upper tail interval values for rejecting the null stability hypothesis are larger.

Suggested Citation

  • Ignacio Mauleón, 2022. "Contributions to Risk Assessment with Edgeworth–Sargan Density Expansions (I): Stability Testing," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1074-:d:780626
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    References listed on IDEAS

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    1. León, à ngel & Mencía, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
    2. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Michael J. Wichura, 1988. "The Percentage Points of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(3), pages 477-484, November.
    5. Lee, Tom K Y & Tse, Y K, 1991. "Term Structure of Interest Rates in the Singapore Asian Dollar Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(2), pages 143-152, April-Jun.
    6. Sargan, J D, 1980. "Some Approximations to the Distribution of Econometric Criteria Which are Asymptotically Distributed as Chi-Squared," Econometrica, Econometric Society, vol. 48(5), pages 1107-1138, July.
    7. Lee, Bong-Soo, 1991. "Government deficits and the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 425-443, June.
    8. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "VaR performance during the subprime and sovereign debt crises: An application to emerging markets," Emerging Markets Review, Elsevier, vol. 20(C), pages 23-41.
    9. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    10. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    11. Prucha, Ingmar R & Kelejian, Harry H, 1984. "The Structure of Simultaneous Equation Estimators: A Generalization towards Nonnormal Disturbances," Econometrica, Econometric Society, vol. 52(3), pages 721-736, May.
    12. Ignacio Mauleón, 2010. "Assessing the value of Hermite densities for predictive distributions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(8), pages 689-714, December.
    13. Esther B. Del Brio & Andrés Mora-Valencia & Javier Perote, 2019. "Expected shortfall assessment in commodity (L)ETF portfolios with semi-nonparametric specifications," The European Journal of Finance, Taylor & Francis Journals, vol. 25(17), pages 1746-1764, November.
    14. Ignacio Mauleon & Javier Perote, 2000. "Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 225-239.
    15. Mauleon, Ignacio, 2003. "Financial densities in emerging markets: an application of the multivariate ES density," Emerging Markets Review, Elsevier, vol. 4(2), pages 197-223, June.
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