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Asypmtotic Filtering Theory for Univariate Arch Models

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  • Daniel B. Nelson
  • Dean P. Foster

Abstract

This paper builds on this earlier work by deriving the asymptotic distribution of the measurement error. This allows us to approximate the measurement accuracy of ARCH conditional variance estimates and compare the efficiency achieved by different ARCH models. We are also able to characterize the relative importance of different kinds of misspecification; for example, we show that misspecifying conditional means adds only trivially (at least asymptotically) to measurement error, while other factors (for example, capturing the "leverage effect," accommodating thick tailed residuals, and correctly modelling the variability of the conditional variance process) are potentially much more important. Third, we are able to characterize a class of asymptotically optimal ARCH conditional variance estimates.

Suggested Citation

  • Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers 0129, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0129 Note: AP
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    References listed on IDEAS

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    1. Stein, Jeremy C, 1988. "Takeover Threats and Managerial Myopia," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 61-80, February.
    2. Myers, Stewart C. & Majluf, Nicolás S., 1945-, 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Working papers 1523-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Stewart C. Myers & Nicholas S. Majluf, 1984. "Corporate Financing and Investment Decisions When Firms Have InformationThat Investors Do Not Have," NBER Working Papers 1396, National Bureau of Economic Research, Inc.
    4. Myers, Stewart C. & Majluf, Nicholas S., 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Journal of Financial Economics, Elsevier, vol. 13(2), pages 187-221, June.
    5. Jeremy C. Stein, 1989. "Efficient Capital Markets, Inefficient Firms: A Model of Myopic Corporate Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 104(4), pages 655-669.
    6. Scharfstein, David. & Stein, Jeremy C., 1988. "Herd behavior and investment," Working papers WP 2062-88., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Scharfstein, David S & Stein, Jeremy C, 1990. "Herd Behavior and Investment," American Economic Review, American Economic Association, pages 465-479.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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