PERIODIC OBSERVATIONS OF HARMONIZABLE SYMMETRIC STABLE
SEQUENCES

Lutz Klotz

Manfred Riedel

Abstract: For harmonizable symmetric stable sequences we solve the following prediction
problem: Assume that the values of the sequence are known at all odd integers. Compute the
metric projection of an unknown value onto the space spanned by the known values as well as
the corresponding approximation error. We study several questions related to this prediction
problem such as regularity and singularity, Wold type decomposition, interrelations
between the spaces spanned by the values at the even and odd integers, respectively.

2000 AMS Mathematics Subject Classification: 60G25, 60G10, 42A10.

Key words and phrases: Harmonizable symmetric stable sequences, linear prediction,
metric projection, Wold type decomposition.