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Harmonic analysis, time series variations and the distributional properties of financial ratios


  • Fuller-Love, N.
  • Rhys, H.
  • Tippett, M.


This paper models the behaviour of financial ratios using the techniques of continuous time stochastic calculus. Previous work in the area has been restricted to models based on first order stochastic differential equations. However, in the present paper we model a ratio's displacement from its long term mean in terms of a second order stochastic differential equation. In this way we show that higher order equations may be used to provide more flexible modelling procedures than those previously studied. The paper begins by describing a ratio's evolution in terms of a particular form of second order stochastic differential equation. A solution is then obtained for this equation. We then show how the parameters of the model may be estimated from a given set of empirical data. The model is then applied to a data set of four ratios for 118 UK companies covering a period of 37 years. For three of the four ratios, clear evidence of a period emerges. Previous work suggests that these ratios are well described by mean reversion processes. Our empirical analysis, however, suggests there is a significant tendency for adjustments to 'overshoot' the targeted long term mean. Taken together with prior work in the area, the paper begins to provide a broad picture of the way in which financial ratios evolve over time.

Suggested Citation

  • Fuller-Love, N. & Rhys, H. & Tippett, M., 1995. "Harmonic analysis, time series variations and the distributional properties of financial ratios," Omega, Elsevier, vol. 23(4), pages 419-427, August.
  • Handle: RePEc:eee:jomega:v:23:y:1995:i:4:p:419-427

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    References listed on IDEAS

    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. De Bondt, Werner F M & Thaler, Richard, 1985. " Does the Stock Market Overreact?," Journal of Finance, American Finance Association, vol. 40(3), pages 793-805, July.
    4. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

    1. Barniv, Ran & Mehrez, Abraham & Kline, Douglas M., 2000. "Confidence intervals for controlling the probability of bankruptcy," Omega, Elsevier, vol. 28(5), pages 555-565, October.
    2. Moon, Tae Hee & Sohn, So Young, 2008. "Technology scoring model for reflecting evaluator's perception within confidence limits," European Journal of Operational Research, Elsevier, vol. 184(3), pages 981-989, February.


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