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ARCH and GARCH models vs. martingale volatility of finance market returns

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  • McCauley, Joseph L.

Abstract

ARCH and GARCH models assume either i.i.d. or 'white noise' as is usual in regression analysis, while also assuming memory in a conditional mean square fluctuation with stationary increments. We will show that ARCH/GARCH is inconsistent with uncorrelated increments, violating the i.i.d. and 'white' assumptions, and violating finance data and the efficient market hypothesis as well.

Suggested Citation

  • McCauley, Joseph L., 2009. "ARCH and GARCH models vs. martingale volatility of finance market returns," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 151-153, September.
    • Handle: RePEc:eee:finana:v:18:y:2009:i:4:p:151-153
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    1. J. Barkley Rosser Jr. (ed.), 2009. "Handbook of Research on Complexity," Books, Edward Elgar Publishing, number 3625.
    2. Katarina Juselius & Ronald MacDonald, 2000. "International Parity Relationships between Germany and the United States: A Joint Modelling Approach," Discussion Papers 00-10, University of Copenhagen. Department of Economics.
    3. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2008. "Empirically based modeling in financial economics and beyond, and spurious stylized facts," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 767-783, December.
    4. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, detrending data, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 202-216.
    5. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
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