Recursive condition for positivity of the angle for multivariate stationary sequences

Authors:
A. Makagon, A. G. Miamee and B. S. W. Schröder

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1821-1825

MSC (1991):
Primary 60G12, 60G25

DOI:
https://doi.org/10.1090/S0002-9939-98-04245-2

MathSciNet review:
1443841

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note a recursive type condition for positivity of the angle between past and future for -variate stationary sequences is provided. In the case it gives a simple different proof of a result due to Solev and Tserkhtsvadze on basicity of bivariate stationary sequences.

**1.**Fefferman, C. (1971). Characterizations of bounded mean oscillation. Bull. Amer. Math. Soc. 77, 587-588. MR**43:6713****2.**Hunt, R. A., Muckenhoupt, B. and Wheeden, R. L. (1973), Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math Soc. 176, 227-251. MR**47:701****3.**Makagon, A. and Salehi, H. (1989), Notes on infinite dimensional stationary sequences. Probability Theory on Vector Spaces IV, Lecture Notes in Math. 1391, Springer-Verlag, 200-238. MR**91i:60103****4.**Masani, P. and Wiener, N. (1957-58), The prediction theory of multivariate stochastic processes I and II, Acta Math. 98, 111 - 150, and 99, 93 - 137. MR**20:4323**; MR**20:4325****5.**Miamee, A. G. (1986), On the Angle between Past and Future for Multivariate Stationary Stochastic Processes, J. Mult. Anal. 20, 205 - 219. MR**88f:60074****6.**Miamee, A. G. and Pourahmadi, M. (1987), Degenerate multivariate stationary processes: Basicity, Past and Future and Autoregressive Representation, Sankhya Ser A. 49, 316-334. MR**91b:62185****7.**Pousson, H. R. (1968). Systems of Toeplitz operators on , II, Trans. Amer. Math. Soc. 133, 527 - 536. MR**37:3377****8.**Solev, V. N. and Tserkhtsvadze, K. A. (1986), A condition for a stationary vector sequence to be a basis (Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 153. MR**88b:60096**

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Additional Information

**A. Makagon**

Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668

Email:
makagon@huajai.cs.hamptonu.edu

**A. G. Miamee**

Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668

Email:
miamee@cs.hamptonu.edu

**B. S. W. Schröder**

Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 26668

Address at time of publication:
Program of Mathematics and Statistics, Louisiana Technical University, Ruston, Louisiana 71272

Email:
Schroder@engr.LaTech.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04245-2

Keywords:
Multivariate stationary sequence,
prediction theory,
positive angle

Received by editor(s):
April 26, 1996

Received by editor(s) in revised form:
December 4, 1996

Additional Notes:
This research was supported by ONR Grant No. N 00014 - 89 - J - 1824

The second author was supported by Army Research Office grant DAAH 04-96-1-0027

The third author was supported by ONR Grant No. N 00014 - 95 - 1 - 0660

Communicated by:
Stanley Sawyer

Article copyright:
© Copyright 1998
American Mathematical Society