DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES

Abstract. In this paper, we shall consider the case where a stationary vector process {X_t} belongs to one of two categories described by two hypotheses π₁ and π₂. These hypotheses specify that {X_t} has spectral density matrices f(Λ) and g(Λ) under π₁ and π₂, respectively. Although Gaussianity of {X_t} is not assumed, we can formally make the Gaussian likelihood ratio (GLR) based on X(1),…X(T). Then an approximation I(f:g) of the GLR is given in terms of f(Λ) and g(Λ). If f(Λ) and g(Λ) are known, we can use I(f:g) as a classification statistic. It is shown that I(f:g) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as T→∝. When g is contiguous to f, we discuss non‐Gaussian robustness of I(f:g). A sufficient condition for the non‐Gaussian robustness will be given. Also a numerical example will be given.