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Approximating Moments by Nonlinear Transformations

  • Karim M. Abadir

    (Imperial College London, UK)

  • Adriana Cornea

    (Imperial College London, UK)

We provide a methodology to calculate the expectation of a variate x in terms of the moments of a transformation of x. Apart from the intrinsic interest in such a fundamental relation that relates the moments of a variate and its nonlinear transformations, our results can be used in practice to approximate E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To obtain an accurate evaluation of the remainder, we derive results for the bounding of functions of complex variables. Our results are useful, for example, in resampling applications like bootstrap confidence intervals for fat-tailed data. They are also useful in economics and finance in quantifying the effect of taking nonlinear transformations on moment conditions and on asset prices which are formulated as expectations.

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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 22_12.

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Date of creation: Jun 2012
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Handle: RePEc:rim:rimwps:22_12
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  1. Ian W. R. Martin, 2008. "Disasters and the Welfare Cost of Uncertainty," American Economic Review, American Economic Association, vol. 98(2), pages 74-78, May.
  2. David Backus & Mikhail Chernov & Ian Martin, 2009. "Disasters implied by equity index options," NBER Working Papers 15240, National Bureau of Economic Research, Inc.
  3. Abadir, K.M. & Magnus, J.R., 2001. "Notation in Econometrics : A Proposal for a Standard," Discussion Paper 2001-8, Tilburg University, Center for Economic Research.
  4. Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, Exeter University, Department of Economics.
  5. Abadir, Karim M. & Talmain, Gabriel, 2005. "Autocovariance functions of series and of their transforms," Journal of Econometrics, Elsevier, vol. 124(2), pages 227-252, February.
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