Stoffer et al. [1] proposed a way of scaling categorical time series data and presented the frequency domain framework called Spectrum Envelope (SpecEnv). SpecEnv can be understood as the largest proportion of the total power, with the maximum achieved by the scaling parameters. We consider this a similar concept to the portfolio approach to measure risk diversification proposed by Meucci [4]. In this article, we explore the relationship between SpecEnv and the diversification index and, moreover, provide a portfolio estimation of spectral density. Furthermore, we apply this portfolio estimation to the study of DNA sequences and confirm its consistency with the results shown in Stoffer et al. [2].

spectral envelope, frequency domain, DNA sequence data, mean-variance portfolio, principle portfolio, diversification management.