![](images/spacer.gif) |
|
|
| | | | | |
|
|
|
|
|
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.
|
Full text: PDF
Pages: 113-120
Published on: March 2, 2008
|
Bibliography
-
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)
-
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)
-
J.P. Burg. Maximum entropy spectral analysis. (1975) Ph.D. Thesis, Department of Geophysics, Stanford University. Math. Review number not available.
-
C. Chatfield. Inverse autocorrelations. J. Roy. Statist. Soc. Ser. A , 142 (1979), 363--377. MR0547168 (81i:62165)
-
P. Cheridito, H. Kawaguchi, and M. Maejima. Fractional Ornstein-Uhlenbeck processes. Electron. J. Probab , 8 (2003), 1--14. MR1961165 (2003m:60096)
-
T.M. Cover, and J.A. Thomas. Elements of information theory. (1991) John Wiley and Sons, New York. MR1122806 (92g:94001)
-
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)
-
W. Feller. Completely monotone functions and sequences. Duke Math. J. , 5 (1939), 661--674. MR0000315 (1,52e)
-
C.W.J. Granger. Long memory relationships and the aggregation of dynamic models. J. Econometrics , 14 (1980), 227--238. MR0597259(81m:62165)
-
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)
-
B. Harris. Determining bounds on integrals with applications to cataloging problems. Ann. Math. Statist., 30 (1959), 521--548. MR0102876(21 #1662)
-
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)
-
S. Kalrin, and L.S. Shapley. The geometry of moment spaces. Memoirs of the American Mathematical Society, 12 (1952) MR0059329(15,512c)
-
R. McVinish. On the structure and estimation of reflection positive processes. J. Appl. Prob., 45 (2008), to appear. Math. Review number not available.
-
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)
-
R. Ranga Rao. Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist., 32 (1962), 659--680. 0137809
(25 #1258)
-
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
-
D.V. Widder. The Laplace Transform. (1946) Princeton University Press. MR0005923(3,232d)
-
P, Zaffaroni. Contemporaneous aggregation of linear dynamic models in large economies. J. Econometrics , 120 (2004), 75--102. 2047781(2004m:62205)
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|