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SEMIFAR Models, with Applications to Commodities, Exchange Rates and the Volatility of Stock Market Indices

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Author Info

  • Jan Beran

    ()
    (Center of Finance and Econometrics)

  • Yuanhua Feng

    ()
    (Center of Finance and Econometrics)

  • Günter Franke

    ()
    (Center of Finance and Econometrics)

  • Dieter Hess

    ()
    (Stern School of Business)

  • Dirk Ocker

    (Center of Finance and Econometrics)

Abstract

The distinction between stationarity, difference stationarity, deterministic trends as well as between short- and long-range dependence has a major impact on statistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. In this paper, recent results on so-called SEMIFAR models introduced by Beran(1999) are summarized and their potential usefulness for economic time series analysis is illustrated by analyzing several commodities, exchange rates, the volatility of stock market indices and some simulated series. SEMIFAR models provide a unified approach that allows for simultaneous modelling of and distinction between deterministic trends, difference stationarity and stationarity with short- and long-range dependence. An iterative data-driven algorithm combines MLE and kernel estimation. Predictions combine stochastic prediction of the random part with functional extrapolation of the deterministic part.

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Bibliographic Info

Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 99-18.

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Length: 36 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:knz:cofedp:9918

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References

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  1. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
  2. Chiu, Shean-Tsong, 1989. "Bandwidth selection for kernel estimate with correlated noise," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 347-354, September.
  3. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, EconWPA.
  4. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Paper 99-01, Center of Finance and Econometrics, University of Konstanz.
  5. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(2), pages 291-311, June.
  6. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
  7. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
  8. Fong, Wai Mun & Ouliaris, Sam, 1995. "Spectral Tests of the Martingale Hypothesis for Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 255-71, July-Sept.
  9. Liu, Christina Y & He, Jia, 1991. " A Variance-Ratio Test of Random Walks in Foreign Exchange Rates," Journal of Finance, American Finance Association, vol. 46(2), pages 773-85, June.
  10. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
  11. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-36, August.
  12. Granger, Clive W. J. & Ding, Zhuanxin, 1996. "Varieties of long memory models," Journal of Econometrics, Elsevier, vol. 73(1), pages 61-77, July.
  13. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  14. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  15. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
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Cited by:
  1. Jan Beran & Yuanhua Feng, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Paper 99-08, Center of Finance and Econometrics, University of Konstanz.
  2. Jan Beran & Dirk Ocker, 1999. "Volatility of Stock Market Indices - An Analysis based on SEMIFAR Models," CoFE Discussion Paper 99-14, Center of Finance and Econometrics, University of Konstanz.

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