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Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distribution

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  • Stavros Stavroyiannis

Abstract

We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined via application of several statistical tests and risk measures. The results indicate that the APARCH model with the standardized Pearson type IV distribution is accurate, within the general financial risk modeling perspective, providing the financial analyst with an additional skewed distribution for incorporation in the risk management tools.

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  • Stavros Stavroyiannis, 2016. "Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distribution," Papers 1602.05749, arXiv.org.
    • Handle: RePEc:arx:papers:1602.05749
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    1. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1586-1609, November.
    2. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
    3. Bhattacharyya, Malay & Chaudhary, Abhishek & Yadav, Gaurav, 2008. "Conditional VaR estimation using Pearson's type IV distribution," European Journal of Operational Research, Elsevier, vol. 191(2), pages 386-397, December.
    4. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    5. Fabio Pizzutilo, 2012. "Use of the Pearson System of Frequency Curves for the Analysis of Stock Return Distributions: Evidence and Implications for the Italian Market," Economics Bulletin, AccessEcon, vol. 32(1), pages 272-281.
    6. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    7. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 84-108.
    8. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    9. 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.
    10. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    11. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    12. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    13. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Nagahara, Yuichi, 1999. "The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 251-264, July.
    16. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    17. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    18. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    19. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    20. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259, September.
    21. F. Pizzutilo, 2012. "The behaviour of the distributions of stock returns: an analysis of the European market using the Pearson system of continuous probability distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(20), pages 1743-1752, October.
    22. Matteo Grigoletto & Francesco Lisi, 2011. "Practical implications of higher moments in risk management," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 487-506, November.
    23. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259.
    24. Bhattacharyya, Malay & Madhav R, Siddarth, 2012. "A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns," MPRA Paper 54189, University Library of Munich, Germany.
    25. Stavros Stavroyiannis & Leonidas Zarangas, 2013. "Out of Sample Value-at-Risk and Backtesting with the Standardized Pearson Type-IV Skewed Distribution," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 60(2), pages 231-247, April.
    26. Phillips,Garry D. A. & Tzavalis,Elias (ed.), 2007. "The Refinement of Econometric Estimation and Test Procedures," Cambridge Books, Cambridge University Press, number 9780521870535.
    27. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    28. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    29. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    30. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    31. Kurt Brannas & Niklas Nordman, 2003. "Conditional skewness modelling for stock returns," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 725-728.
    32. Gamini Premaratne, 2005. "A Test for Symmetry with Leptokurtic Financial Data," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 169-187.
    33. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    34. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, vol. 2(Apr), pages 39-69.
    35. Malay Bhattacharyya & Nityanand Misra & Bharat Kodase, 2009. "MaxVaR for non-normal and heteroskedastic returns," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 925-935.
    36. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1586-1609.
    37. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    38. Matteo Grigoletto & Francesco Lisi, 2009. "Looking for skewness in financial time series," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 310-323, July.
    39. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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