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Model-Free Volatility Prediction

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  • Politis, Dimitris N.

Abstract

The well-known ARCH/GARCH models with normal errors account only partly for the degree of heavy tails empirically found in the distribution of financial returns series. Instead of resorting to an arbitrary nonnormal distribution for the ARCH/GARCH residuals we propose a different viewpoint via a novel normalizing and variance– stabilizing transformation (NoVaS) that can be seen as an alternative to parametric modeling. Some properties of this transformation are discussed, and algorithms for optimizing it are given. Special emphasis is given on the problem of volatility prediction and the issue of a proper measure for quality of prediction. A new prediction algorithm with favorable performance is given based on the NoVaS transformation. For motivation and illustration of this new general methodology, the NoVaS transformation is implemented in connection with three real data series: a foreign exchange series (Yen vs. Dollar), a stock index series (S&P500 index), and a stock price series (IBM).

Suggested Citation

  • Politis, Dimitris N., 2003. "Model-Free Volatility Prediction," University of California at San Diego, Economics Working Paper Series qt0648834b, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt0648834b
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
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    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
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    Cited by:

    1. Dimitris N. Politis & Dimitrios D. Thomakos, 2007. "NoVaS Transformations: Flexible Inference for Volatility Forecasting," Working Paper series 44_07, Rimini Centre for Economic Analysis.
    2. Politis, D N, 2006. "Can the Stock Market be Linearized?," University of California at San Diego, Economics Working Paper Series qt8th5q5hq, Department of Economics, UC San Diego.
    3. Dimitrios Thomakos & Johannes Klepsch & Dimitris N. Politis, 2020. "Model Free Inference on Multivariate Time Series with Conditional Correlations," Stats, MDPI, vol. 3(4), pages 1-26, November.

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