Discriminant analysis for locally stationary processes

• Authors: Kenji Sakiyama;Masanobu Taniguchi
• Venue: Journal of Multivariate Analysis
• Year: 2004

In this paper, we discuss discrinant analysis for locally stationary processes, which constitute a class of non-stationary processes. Consider the case where a locally stationary process {Xt,T} belongs to one of two categories described by two hypotheses π1 and π2. Here T is the length of the observed stretch. These hypotheses specify that {Xt,T} has time-varying spectral densities f(u, λ) and g(u, λ) under π1 and π2, respectively. Although Gaussianity of {Xt,T} is not assumed, we use a classification criterion D(f : g). which is an approximation of the Gaussian likelihood ratio for {Xt,T} between π1 and π2. Then it is shown that D(f : g) is consistent, i.e., the misclassification probabilities based on D(f : g) converge to zero as T → ∞. Next, in the case when g(u, λ) is contiguous to f(u, λ). we evaluate the misclassification probabilities, and discuss non-Gaussian robustness of D(f : g). Because the spectra depend on time, the features of non-Gaussian robustness are different from those for stationary processes. It is also Interesting to investigate the behavior of D(f : g) with respect to infinitesimal perturbations of the spectra. Introducing an influence function of D(f : g). we illuminate its infinitesimal behavior. Some numerical studies are given.