Time series analysis under stationary assumption has been well established. However, stationary time series models are not plausible to describe the real world. Indeed, relatively long stretches of time series data should contain either slow or rapid changes in the spectra. To develop a general non-stationary theory, we have to pay careful attention to constituting a suitable model, otherwise the observations obtained in the future give no information about the present structure. Dahlhaus [1–4] has introduced an important class of non-stationary processes, called locally stationary processes which have the time varying spectral densities. In this paper, for a clustering problem of stock returns in Tokyo Stock Exchanges, we propose nonparametric approach based on generalized integral functional measures of the time varying spectral densities. The generalized measures include Gaussian Kullback–Leibler information and Chernoff information measures. The clustering results well extract the features of the relationship among the companies.
Surface of Maximums of AR(2) Process Spectral Densities and its Application in Time Series Statistics