Optimising prediction error among completely monotone covariance sequences

Ross S McVinish (Queensland University of Technology)

Abstract


We provide a characterisation of Gaussian time series which optimise the one-step prediction error subject to the covariance sequence being completely monotone with the first m covariances specified.

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Pages: 113-120

Publication Date: March 2, 2008

DOI: 10.1214/ECP.v13-1355

References

  1. O.E. Barndorff-Neilsen, J.L. Jensen, and M. Sorensen. Some stationary processes in discrete and continuous time. Adv. in Appl. Probab. 30 (1995), 989--1007. MR1671092 (2000b:60092)
  2. O.E. Barndorff-Neilsen, N. and Shephard. Non-Gaussian Ornstein-Uhlenbeck based models and some of their uses in financial econometrics (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. , 63 (2001), 167--241. MR1841412 (2002c:62127)
  3. J.P. Burg. Maximum entropy spectral analysis. (1975) Ph.D. Thesis, Department of Geophysics, Stanford University. Math. Review number not available.
  4. C. Chatfield. Inverse autocorrelations. J. Roy. Statist. Soc. Ser. A , 142 (1979), 363--377. MR0547168 (81i:62165)
  5. P. Cheridito, H. Kawaguchi, and M. Maejima. Fractional Ornstein-Uhlenbeck processes. Electron. J. Probab , 8 (2003), 1--14. MR1961165 (2003m:60096)
  6. T.M. Cover, and J.A. Thomas. Elements of information theory. (1991) John Wiley and Sons, New York. MR1122806 (92g:94001)
  7. D. Dacunha-Castelle, and L. Ferm'{i}n. Disaggregation of long memory processes on $ mathcal{C}^{infty} $ class. Electron. Comm. Probab., 11 (2006), 35--44. MR2219344(2007i:62111)
  8. W. Feller. Completely monotone functions and sequences. Duke Math. J. , 5 (1939), 661--674. MR0000315 (1,52e)
  9. C.W.J. Granger. Long memory relationships and the aggregation of dynamic models. J. Econometrics , 14 (1980), 227--238. MR0597259(81m:62165)
  10. C.W.J. Granger, and R. Joyeux, An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal., 1 (1980), 15--29. MR0605572 (82d:62140)
  11. B. Harris. Determining bounds on integrals with applications to cataloging problems. Ann. Math. Statist., 30 (1959), 521--548. MR0102876(21 #1662)
  12. E. Igloi, and G. Terdik. Long-range dependence through Gamma-mixed Ornstein-Uhlenbeck processes. Electron. J. Probab., 4(16) (1999), 1--33. MR1713649 (2000m:60060)
  13. S. Kalrin, and L.S. Shapley. The geometry of moment spaces. Memoirs of the American Mathematical Society, 12 (1952) MR0059329(15,512c)
  14. R. McVinish. On the structure and estimation of reflection positive processes. J. Appl. Prob., 45 (2008), to appear. Math. Review number not available.
  15. G. Oppenheim, and M.-C. Viano. Aggregation of random parameters Ornstein-Uhlenbeck or AR processes: some convergence results. J. Time Ser. Anal., 25 (2004), 335--350. MR2062677 (2005f:62143)
  16. R. Ranga Rao. Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist., 32 (1962), 659--680. 0137809 (25 #1258)
  17. G.O. Roberts, O. Papaspiliopoulos, and P. Dellaportas. Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes. J. R. Stat. Soc. Ser. B Stat. Methodol. , 66 (2004), 369--393. MR2062382
  18. D.V. Widder. The Laplace Transform. (1946) Princeton University Press. MR0005923(3,232d)
  19. P, Zaffaroni. Contemporaneous aggregation of linear dynamic models in large economies. J. Econometrics , 120 (2004), 75--102. 2047781(2004m:62205)
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