Applications of a finitedimensional duality principle to some prediction problems
Preprint Series # 871 Kasahara, Yukio and Pourahmadi, Mohsen and Inoue, Akihiko Applications of a finitedimensional duality principle to some prediction problems. (2007); AbstractSome of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in Hilbert spaces of analytic functions (Nakazi, 1984) to linear regression in statistics (Box and Tiao, 1975). We unify these results via a finitedimensional duality lemma and elementary ideas from the linear algebra. The approach reveals the inherent finitedimensional character of many difficult prediction problems, the role of duality and biorthogonality for a finite set of random variables. The lemma is particularly useful when the number of missing values is small, like one or two, as in the case of Kolmogorov and Nakazi prediction problems. The stationarity of the underlying process is not a requirement. It opens up the possibility of extending such results to nonstationary processes. Item Type:  Preprint 

Additional Information:  20 

Uncontrolled Keywords:  Finite prediction problems, biorthogonality and duality,
missing values, stationary time series, Wold decomposition 

Subjects:  60xx PROBABILITY THEORY AND STOCHASTIC PROCESSES 

ID Code:  1767 

