Local Whittle estimation of multi-variate fractionally integrated processes

Journal of Time Series Analysis

Volumn 32, Issue 3, 2011, Pages 317-335

  Nielsen, Frank S ^a  

^a Dong Energy and Creates ^*  (Denmark)

Author keywords

C14; C32; Exchange rates; Fractional integration; Local whittle; Long memory; Multi variate semi parametric estimation

Indexed keywords

EID: 79954431306     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2010.00702.x     Document Type: Article

References (31)

1. Abadir, K. M., Distaso, W. and Giraitis, L. (2007) Nonstationarity-extended local Whittle estimation. Journal of Econometrics 141, 1353-84.
2. Andrews, D. W. K. and Sun, Y. (2004) Adaptive local polynomial Whittle estimation of long-range dependence. Econometrica 72, 569-614.
3. Baillie, R. T. (1996) Long memory processes and fractional integration in econometrics. Journal of Econometrics 73, 5-59.
4. Baillie, R. T. and Bollerslev, T. (1989) The message in daily exchange rates: a conditional variance tale. Journal of Business and Economic Statistics 7, 297-305.
5. Baillie, R. T. and Bollerslev, T. (1994) Cointegration, fractional cointegration, and exchange rate dynamics. Journal of Finance 49, 737-45.
6. Dalla, V., Giraitis, L. and Hidalgo, J. (2006) Consistent estimation of the memory parameter for nonlinear time series. Journal of Time Series Analysis 27, 211-51.
7. Davidson, J. and Hashimzade, N. (2009) Type I and type II fractional brownian motions: a reconsideration. Computational Statistics and Data Analysis 53, 2089-106.
8. Diebold, F. X., Gardeazabal, J. and Yilmaz, K. (1994) On cointegration and exchange rate dynamics. Journal of Finance 49, 727-35.
9. Hosking, J. R. M. (1981) Fractional differencing. Biometrika 68, 165-76.
10. Hurvich, C. M. and Chen, W. W. (2000) An efficient taper for potentially overdifferenced long-memory time series. Journal of Time Series Analysis 21, 155-80.
11. Hurvich, C. M. and Ray, B. K. (1995) Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. Journal of Time Series Analysis 16, 17-41.
12. Kim, C. and Phillips, P. (2000) Modified log periodogram regression. Working Paper, Yale University.
13. Kim, C. S. and Phillips, P. C. B. (2006) Log periodogram regression: the nonstationary case. Cowles Foundation Discussion Papers 1587, Cowles Foundation, Yale University.
14. Künsch, H. R. (1987) Statistical aspects of self-similar processes. In Proceedings of the First World Congress of the Bernoulli Society (eds Y. Prokhorov and V. V. Sazanov ). Utrecht: VNU Science Press, pp. 67-74.
15. Lahiri, S. N. (2003) A necessary and sufficient condition for asymptotic independence of discrete fourier transforms under short- and long-range dependence. Annals of Statistics 31, 613-41.
16. Lobato, I. N. (1999) A semiparametric two-step estimator in a multivariate long memory model. Journal of Econometrics 73, 303-24.
17. Lobato, I. N. and Velasco, C. (2000) Long memory in stock-market trading volume. Journal of Business and Economic Statistics 18, 570-6.
18. Marinucci, D. and Robinson, P. M. (1999) Alternative forms of fractional brownian motion. Journal of Statistical Planning and Inference 21, 685-705.
19. Nielsen, F. S. (2008) Local polynomial Whittle estimation covering nonstationary fractional processes. CREATES RP 2008-28, University of Aarhus.
20. Nielsen, M. Ø. (2004) Optimal residual-based tests for fractional cointegration and exchange rate dynamics. Journal of Business & Economic Statistics 22, 331-45.
21. Nielsen, M. Ø. and Shimotsu, K. (2007) Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach. Journal of Econometrics 127, 574-96.
22. Phillips, P. C. B. (1999) Discrete fourier transformation of fractional processes. Discussion Paper 1243, Yale University (Cowles Foundation).
23. Phillips, P. C. B. and Shimotsu, K. (2004) Local Whittle estimation in nonstationary and unit root cases. Annals of Statistics 32, 656-92.
24. Robinson, P. M. (1994) Rates of convergence and optimal spectral bandwidth for long range dependence. Probability Theory and Related Fields 99, 443-73.
25. Robinson, P. M. (1995a) Gaussian semiparametric estimation of long range dependence. Annals of Statistics 23, 1630-61.
26. Robinson, P. M. (1995b) Log-periodogram regression of time series with long range dependence. Annals of Statistics 23, 1048-72.
27. Robinson, P. M. (2008) Multiple local Whittle estimation in stationary systems. Annals of Statistics 36, 2508-30.
28. Shimotsu, K. (2007) Gaussian semiparametric estimation of multivariate fractionally integrated processes. Journal of Econometrics 137, 277-310.
29. Shimotsu, K. and Phillips, P. (2005) Exact local Whittle estimation of fractional integration. The Annals of Statistics 33, 1890-933.
30. Velasco, C. (1999a) Gaussian semiparametric estimation of non-stationary time series. Journal of Time Series Analysis 20, 87-127.
31. Velasco, C. (1999b) Non-stationary log-periodogram regression. Journal of Econometrics 91, 325-71.