IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Imparting structural instability to mortality forecasts: Testing for sensitive dependence on initial conditions with innovations

Listed author(s):
  • Lawrence Carter
Registered author(s):

    This article explores a nontraditional approach to examining the problem of forecast uncertainty in extrapolative demographic models. It builds on prior research on stochastic time series forecast models, but diverges to examine their deterministic counterparts. The focus here is an examination of the structural integrity of the Lee-Carter (1992) method applied to mortality forecasts. I investigate the nonlinear dynamics of the Lee-Carter method, particularly its sensitive dependence of the forecasts on the initial conditions of the model. I examine the Lee-Carter nonlinear demographic model, mx,t — exp (ax+ bxkt + ex,t), which is decomposed using SVD to derive a single time-varying linear index of mortality, kt. From a 90 year time series of kt, forty nine 40 year realizations are sampled. These realizations are modeled and estimated using Box-Jenkins techniques. The estimated parameters of these realizations and the first case of each of the samples are the initial conditions for the iterations of nonlinearized transformation of k, to exp (kt). The terminal year for each of the 49 iterated series is 2065. The deterministic nonlinear dynamics of this system of 49 iterated series is investigated by testing its Lyapunov exponents as a nonparametric diagnostic of a one dimensional dynamical system. The exponents are all negative, indicating that chaos is not prevalent in this system. The nonexistence of chaos suggests stability in the model and reaffirms the predictability of this one dimensional map. Augmenting the iterations of the initial conditions with additive stochastic innovations, {et, t ≥ 1}, creates a stochastic dynamical system of the form, kt = kt,-1 — c + ϕ flu +et. Here, et is treated as a surrogate for some unanticipated time series event (e.g. an epidemic) that impacts the deterministic map. Gaussian white noise innovations do not move the iterations far from equilibrium and only for short time intervals. So, stepping the mean of the innovations by .01 produces stable Lyapunov exponents until the mean equals .35 where some of the exponents are positive. At this point, deterministic chaos is evident, implying instability in the forecasts. The substantive implications of this instability are discussed.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Taylor & Francis Journals in its journal Mathematical Population Studies.

    Volume (Year): 8 (2000)
    Issue (Month): 1 ()
    Pages: 31-54

    in new window

    Handle: RePEc:taf:mpopst:v:8:y:2000:i:1:p:31-54
    DOI: 10.1080/08898480009525472
    Contact details of provider: Web page:

    Order Information: Web:

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:taf:mpopst:v:8:y:2000:i:1:p:31-54. 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: (Chris Longhurst)

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.