IDEAS home Printed from
   My bibliography  Save this paper

Spectral Implications of Security Market Data for Models of Dynamic Economies


  • Christopher Otrok, B. Ravikumar, Charles H. Whiteman


Hansen and Jagannathan (1991) proposed a volatility bound for evaluating asset-pricing models that is a restriction on the volatility of a representative agentÌs intertemporal marginal rate of substitution (IMRS). We develop a generalization of their bound that (i) incorporates the serial correlation properties of return data and (ii) allows us to calculate a spectral version of the bound. That is, we develop a bound and then decompose it by frequency; this enables us to judge whether models match important aspects of the data in the long run, at business cycle frequencies, seasonal frequencies, etc. Our generalization is related to the space in which the bounding IMRS lives. Instead of specifying the bounding IMRS to be a linear combination of contemporaneous returns, we let the bounding IMRS live in a linear space of current, past and future returns. We also require the bounding IMRS to satisfy additional restrictions that resemble Euler equations. Our volatility bound not only uses the unconditional first and second moment properties of return data but also the serial correlation properties. Incorporating this additional information results in a tighter bound for two reasons. First, we impose additional orthogonality conditions on our bounding IMRS. Second, our projection is onto a larger space (current, past and future returns). We also show that the spectrum of the model IMRS must exceed the spectrum of our bounding IMRS. Using the serial correlation properties of returns (together with the mean and variance), we are able to derive the spectrum of the bounding IMRS. That is, the lower bound on the spectrum of the model IMRS is completely pinned down by asset return data. This permits a frequency-by-frequency examination of the fundamental component of the model, namely, the Euler equation that links asset returns to the IMRS. In particular, we can identify the frequencies at which an asset-pricing model does not perform well. The researcher can then decide whether or not failures at a particular set of frequencies are troubling. We illustrate our method with four asset pricing models -- time-separable CRRA preferences, state non-separable preferences (Epstein-Zin, 1989, 1991), internal habit formation (Constantinides, 1990), and external habit formation preferences (Campbell and Cochrane, 1999) -- using two data sets, annual data from 1889-1992 and quarterly data spanning 1950:1-1995:4.

Suggested Citation

  • Christopher Otrok, B. Ravikumar, Charles H. Whiteman, 2001. "Spectral Implications of Security Market Data for Models of Dynamic Economies," Computing in Economics and Finance 2001 71, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:71

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item


    spectrum; volatility bound; asset pricing; model evaluation;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf1:71. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.