Development of a new prediction-theoretic method for stochastic fields, with applications to finance

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654037
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Hiroshima University
• Principal Investigator: INOUE AKIHIKO 広島大学, 理学(系)研究科(研究院), 教授 (50168431)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 有限予測係数 / 偏相関関数 / 多次元弱定常過程 / Baxter の不等式 / 予測理論

Outline of Final Research Achievements

A. Inoue, with Y. Kasahara and M. Pourahmadi, considered an intersection of past and future property (IPF) of multivariate stationary processes. The importance of (IPF) for univariate stationary processes is that it, combined with von Neumann's Alternating Projection Theorem, allows one to derive explicit and useful representations of finite-past prediction error variances, finite-past prediction coefficients, and partial autocorrelation functions. They showed that it is possible to extend the approach to multivariate stationary processes, and obtained similar representation theorems for multivariate stationary processes with (IPF). They also characterized complete nondeterminism, which is closely related to (IPF), by extending the concept of rigidity to matrix-valued functions.

Free Research Field

確率論