Journal of Applied Probability

Power-law correlations and other models with long-range dependence on a lattice

Chunsheng Ma

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper introduces long-range dependence for a stationary random field on a plane lattice, derives an exact power-law correlation model and other models with long-range dependence on the lattice, and explores the close connection between short-range dependent correlation functions and absolutely summable double sequences.

Article information

Source
J. Appl. Probab. Volume 40, Number 3 (2003), 690-703.

Dates
First available: 24 July 2003

Permanent link to this document
http://projecteuclid.org/euclid.jap/1059060896

Digital Object Identifier
doi:10.1239/jap/1059060896

Mathematical Reviews number (MathSciNet)
MR1993261

Zentralblatt MATH identifier
02066245

Subjects
Primary: 60G60: Random fields
Secondary: 60G10: Stationary processes 62M30: Spatial processes 62M15: Spectral analysis

Keywords
Correlation long-range dependence random field short-range dependence spectral density

Citation

Ma, Chunsheng. Power-law correlations and other models with long-range dependence on a lattice. Journal of Applied Probability 40 (2003), no. 3, 690--703. doi:10.1239/jap/1059060896. http://projecteuclid.org/euclid.jap/1059060896.


Export citation

References

  • Berg, C. and Forst, G. (1975). Potential Theory on Locally Compact Abelian Groups. Springer, New York.
  • Besag, J. (1981). On a system of two-dimensional recurrence equations. J. R. Statist. Soc. B 43, 302--309.
  • Brown, P. E., Diggle, P. J., Lord, M. E. and Young, P. C. (2001). Space--time calibration of radar rainfall data. Appl. Statist. 50, 221--241.
  • Cox, D. R. (1984). Long-range dependence: a review. In Statistics: an Appraisal, eds H. A. David and H. T. David, Iowa State University Press, Ames, IA, pp. 55--74.
  • Cressie, N. A. C. (1993). Statistics for Spatial Data. John Wiley, New York.
  • Donahue, M. J., Brockwell, P. J. and Davis, R. A. (1995). On permissible correlations for locally correlated stationary processes. Statist. Prob. Lett. 22, 49--53.
  • Fairfield Smith, H. (1938). An empirical law describing heterogeneity in the yields of agricultural crops. J. Agricultural Sci. 28, 1--23.
  • Gneiting, T. (2000). Power-law correlations, related models for long-range dependence and their simulation. J. Appl. Prob. 37, 1104--1109.
  • Granger, C. W. J. and Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1, 15--29.
  • Haas, T. C. (1995). Local prediction of a spatio-temporal process with an application to wet sulfate deposition. J. Amer. Statist. Assoc. 90, 1189--1199.
  • Heyde, C. C. and Yang, Y. (1997). On defining long-range dependence. J. Appl. Prob. 34, 939--944.
  • Hosking, J. R. M. (1981). Fractional differencing. Biometrika 68, 165--176.
  • Kashyap, R. L. and Lapsa, P. M. (1984). Synthesis and estimation of random fields using long-correlation models. IEEE Trans. Pattern Anal. Mach. Intell. 6, 800--809.
  • Ma, C. (2002). Correlation models with long-range dependence. J. Appl. Prob. 39, 370--382.
  • Ma, C. (2003a). Families of spatio-temporal stationary covariance models. To appear in J. Statist. Planning Infer.
  • Ma, C. (2003b). Spatio-temporal stationary covariance models. J. Multivariate Anal. 86, 97--107.
  • Martin, R. J. and Eccleston, J. A. (1992). A new model for slowly-decaying correlations. Statist. Prob. Lett. 13, 139--145.
  • Martin, R. J. and Walker, A. M. (1997). A power-law model and other models for long-range dependence. J. Appl. Prob. 34, 657--670.
  • McLeod, A. I. and Hipel, K. W. (1978). Preservation of the rescaled adjusted range, 1: a reassessment of the Hurst phenomenon. Water Resources Res. 14, 491--508.
  • Modjeska, J. S. and Rawlings, J. O. (1983). Spatial correlation analysis of uniformity data. Biometrics 39, 373--384.
  • Moran, P. A. P. (1973). Necessary conditions for Markovian processes on a lattice. J. Appl. Prob. 10, 605--612.
  • Pearce, S. C. (1976). An examination of Fairfield Smith's law of environmental variation. J. Agricultural Sci. 87, 21--24.
  • Rainville, E. D. (1960). Special Functions. Macmillan, New York.
  • Renshaw, E. (1994). The linear spatial-temporal interaction process and its relation to $1/ømega$-noise. J. R. Statist. Soc. B 56, 75--91.
  • Rodriguez-Iturbe, I., Marani, M., D'Odorico, P. and Rinaldo, A. (1998). On space--time scaling of cumulated rainfall fields. Water Resources Res. 34, 3461--3469.
  • Rosenblatt, M. (1985). Stationary Sequences and Random Fields. Birkhäuser, Boston, MA.
  • Whittle, P. (1956). On the variation of yield variance with plot size. Biometrika 43, 337--343.
  • Whittle, P. (1962). Topographic correlation, power-law covariance functions, and diffusion. Biometrika 49, 305--314.