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Modelling the Absolute Returns of Different Stock Indices: Exploring the Forecastability of an Alternative Measure of Risk

  • Granger, Clive W.J.
  • Sin, Chor-yiu

Conventional measures of the risk of a financial asset make use of the unobserved (conditional) variance or standard deviation of its return. In this paper, we treat the observed absolute return as a measure of risk and explore its forecastability. Two simple models are considered. One is a new AR-like model which is applied to the absolute return. The other is an ARCH-like model called Asymmetric Power ARCH. The forecastability is evaluated with the average log-likelihood of absolute return, instead of that of return itself. While the absolute return is interpreted as "volatility", some quantities of its entire distribution, such as the 95-th quantiles, can be interpreted as "volatility of volatility". We apply both models to three stock indices, namely Hang Seng Index, Nikkei 225 Index and Standard and Poors 500 Index. The new model by and large outperforms the ARCH-like model in both in-sample goodness of fit and post-sample forecastability. It performs exceptionally well in the post-sample period after the outbreak of the Asian financial crisis

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt48r4781r.

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Date of creation: 01 Jun 1999
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Handle: RePEc:cdl:ucsdec:qt48r4781r
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  1. 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.
  2. Koenker, Roger, 1992. "When Are Expectiles Percentiles?," Econometric Theory, Cambridge University Press, vol. 8(03), pages 423-424, September.
  3. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-96, June.
  4. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
  5. Cao, C Q & Tsay, R S, 1992. "Nonlinear Time-Series Analysis of Stock Volatilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S165-85, Suppl. De.
  6. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
  7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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