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Trend estimation of financial time series

Author

Listed:
  • Víctor M. Guerrero
  • Adriana Galicia‐Vázquez

Abstract

We propose to decompose a financial time series into trend plus noise by means of the exponential smoothing filter. This filter produces statistically efficient estimates of the trend that can be calculated by a straightforward application of the Kalman filter. It can also be interpreted in the context of penalized least squares as a function of a smoothing constant has to be minimized by trading off fitness against smoothness of the trend. The smoothing constant is crucial to decide the degree of smoothness and the problem is how to choose it objectively. We suggest a procedure that allows the user to decide at the outset the desired percentage of smoothness and derive from it the corresponding value of that constant. A definition of smoothness is first proposed as well as an index of relative precision attributable to the smoothing element of the time series. The procedure is extended to series with different frequencies of observation, so that comparable trends can be obtained for say, daily, weekly or intraday observations of the same variable. The theoretical results are derived from an integrated moving average model of order (1, 1) underlying the statistical interpretation of the filter. Expressions of equivalent smoothing constants are derived for series generated by temporal aggregation or systematic sampling of another series. Hence, comparable trend estimates can be obtained for the same time series with different lengths, for different time series of the same length and for series with different frequencies of observation of the same variable. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Víctor M. Guerrero & Adriana Galicia‐Vázquez, 2010. "Trend estimation of financial time series," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 205-223, May.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:3:p:205-223
    DOI: 10.1002/asmb.763
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    References listed on IDEAS

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    1. Paresh Kumar Narayan & Russell Smyth, 2005. "Are OECD stock prices characterized by a random walk? Evidence from sequential trend break and panel data models," Applied Financial Economics, Taylor & Francis Journals, vol. 15(8), pages 547-556.
    2. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    3. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    4. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    5. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    7. Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    8. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    9. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    10. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    11. Guerrero, Victor M., 2007. "Time series smoothing by penalized least squares," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1225-1234, July.
    12. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
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