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Fractional Integration in the Context of Periodicity: A Monte Carlo Experiment and an Empirical Study

  • Gil-Alana Luis A. (Universidad de NavarraCampus Universitario Facultad de Ciencias Economicas Edificio Biblioteca)
  • 발행 : 2006.12.31

초록

Recent results in applied statistics have shown that the presence of periodicities in time series may influence the estimation and testing of the fractional differencing parameter. In this article, we provide further evidence on the issue by using several procedures of fractional integration. The results show that in the presence of periodicities, the order of integration can be erroneously detected. An empirical application in the context of seasonal data is also carried out at the end of the article.

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참고문헌

  1. Agaikloglou, C., P. Newbold and M. Wohar (1992), Bias in an estimator of the fractional difference parameter. Journal of Time Series Analysis, Vol. 14, 235-246 https://doi.org/10.1111/j.1467-9892.1993.tb00141.x
  2. Baillie, R.T (1996), Long memory processes and fractional integration in econo -rnetrics. Joumal of Econometrics, Vol. 73, 5-59 https://doi.org/10.1016/0304-4076(95)01732-1
  3. Beran, J (1994), Statistics for long memory processes. Chapman and Hall, New York
  4. Beran, J., R. Sherman, M.S. Taqqu and W. Willinger (1995), Long-range dependence in variable-bit-rate video traffic. IEEE Transactions and Communications, Vol. 43, 1566-1579 https://doi.org/10.1109/26.380206
  5. Dahlhaus, R (1989), Efficient parameter estimation for self-similar process. Annals of Statistics, Vol. 17, 1749-1766 https://doi.org/10.1214/aos/1176347393
  6. Fox, R. and M.S. Taqqu (1986), Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics, Vol. 14, 517-532 https://doi.org/10.1214/aos/1176349936
  7. Geweke, J. and S. Porter-Hudak, (1983), The estimation and application of long memory time series models. Journal of Time Series Analysis, Vol. 4, 221-238 https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
  8. Granger, C.W.J (1980), Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, Vol. 14, 227-238 https://doi.org/10.1016/0304-4076(80)90092-5
  9. Granger, C.W.J (1981), Some properties of time series data and their use in econometric model specification. Journal of Econometrics, Vol. 16, 121-130 https://doi.org/10.1016/0304-4076(81)90079-8
  10. Granger, C.W.J. and R. Joyeux (1980), An introduction ot long memory time series and fractionally differencing. Journal of Time Series Analysis, Vol. 1, 15-29 https://doi.org/10.1111/j.1467-9892.1980.tb00297.x
  11. Hauser, M.A (1999), Maximum likelihood estimators for ARFIMA models: A Monte Carlo study. Journal of Statistical Planning and Inference, Vol. 80, 229-255 https://doi.org/10.1016/S0378-3758(98)00252-3
  12. Hosking, J.R.M (1981), Fractional differencing. Biometrika, Vol. 68, 165-176 https://doi.org/10.1093/biomet/68.1.165
  13. Hurst, H.E., (1951), Long-term storage capacity of reservoirs. Transactions of the American Society Civil Engineering, Vol. 116, 770-799
  14. Kunsch, H (1986), Discrimination between monotonic trends and long-range dependence. Journal of Applied Probability, Vol. 23, 1025-1030 https://doi.org/10.2307/3214476
  15. La, A.W (1991), Long-term memory in stock prices. Econometrica, Vol. 59, 1279-1313 https://doi.org/10.2307/2938368
  16. Mandelbrot, B.B (1972), Statistical methodology for non periodic cycles: from the covariance to R/S analysis. Annals of Economic and Social Measurement, Vol. 1, 259-290
  17. Mandelbrot, B.B (1975), Limit theorems on the self-normalized range for weakly and strongly dependent processes, Z. Wahrscheinlichkeitstheorie verw. Geb 31, 271-285 https://doi.org/10.1007/BF00532867
  18. Mandelbrot, B (1977), Fractals: Form, chance and dimension, Freeman, San Francisco
  19. Mandelbrot, B.B. and M.S. Taqqu (1979), Robust R/S analysis of long run serial correlation, Proceedings of the 42nd Session of the International Statistical Institute, Manila
  20. Mandelbrot, B.B. and J.R. Wallis (1968), Noah, Joseph and operational hydrology. Water Resources Research, Vol. 4, 909-918 https://doi.org/10.1029/WR004i005p00909
  21. Mandelbrot, B.B. and J.R. Wallis (1969), Some long run properties of geophysical records. Water Resources Research, Vol. 5, 321-340 https://doi.org/10.1029/WR005i002p00321
  22. Montanari, A, R. Rosso and M.S. Taqqu, (1995), A seasonal fractional differenced ARIMA model: An application to the River Nile monthly flows at Aswan, Preprint
  23. Montanari, A, R. Rosso and M.S. Taqqu (1996), Some long-run properties of rainfall records In Italy. Journal of Geoophysical Research Atmospheres, Vol. 101, 431-438
  24. Montanari, A., R. Rosso and M.S. Taqqu (1997), Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation and simulation. Water Resources Research, Vol. 331, 1035-1044
  25. Montanari, A., M.S. Taqqu and V. Teverovsky (1999), Estimating long range dependence in the presence of periodicity. An empirical study. Mathematical and Computer Modelling, Vol. 29, 217-238 https://doi.org/10.1016/S0895-7177(99)00104-1
  26. Phillips, P.C.B. and K. Shimotsu (2005), Exact local Whittle estimation of fractional integration. Annals of Statistics, Vol. 33, 1890-1933 https://doi.org/10.1214/009053605000000309
  27. Press, W.H., B.P. Flannery, S.A Teukolsky and W.T. Wetterling (1986), Numerical recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge
  28. Robinson, P.M (1978), Statistical inference for a random coefficient autoregre -ssive model, Scandinavian. Journal of Statistics, Vol. 5, 163-168
  29. Robinson, P.M (1994a), Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association, Vol. 89, 1420-1437 https://doi.org/10.2307/2291004
  30. Robinson, P.M (1994b), Semiparametric analysis of long memory time series. Annals of Statistics, Vol. 22, 515-539 https://doi.org/10.1214/aos/1176325382
  31. Robinson, P.M (1995a), Gaussian semiparametric estimation of long range dependence. Annals of Statistics, Vol. 23, 1630-1661 https://doi.org/10.1214/aos/1176324317
  32. Robinson, P.M (1995b), Log-periodogram regression of time series with long range dependence. Annals of Statistics, Vol. 23, 1048-1072 https://doi.org/10.1214/aos/1176324636
  33. Smith, J; Taylor, N. and Yadav, S (1997), Comparing the bias and misspecifi -cation in ARFIMA models. Journal of Time Series Analysis, Vol. 18, 507-527 https://doi.org/10.1111/1467-9892.00065
  34. Sowell, F (1992), Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics, Vol. 53, 165-188 https://doi.org/10.1016/0304-4076(92)90084-5
  35. Velasco, C (1999). Gaussian semiparametric estimation of nonstationary time series. Journal of Time Series Analysis, Vol. 20, 87-127 https://doi.org/10.1111/1467-9892.00127
  36. Willinger, W., M.S. Taqqu, W.E. Leland and D.V. Wilson (1995), Self simil -arity III high-speed packet traffic. Analysis and modelling of ethernet traffic measurements. Statistical Sciences, Vol. 10, 67-85 https://doi.org/10.1214/ss/1177010131