Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Phylogenetic and ecological significance in the evolution of Cetacean tonal sounds

Cetaceans are aquatic mammals that rely primarily on sound for most daily tasks. A compendium of sounds is emitted for orientation, prey detection, and predator avoidance, and to communicate. Communicative sounds are among the most studied Cetacean signals, particularly those referred to as tonal sounds. Because tonal sounds have been studied especially well in social dolphins, it has been assumed these sounds evolved as a social adaptation. However, whistles have been reported in ‘solitary’ species and have been secondarily lost three times in social lineages. Clearly, therefore, it is necessary to examine closely the association, if any, between whistles and sociality instead of merely assuming it. Several hypotheses have been proposed to explain the evolutionary history of Cetacean tonal sounds. The main goal of this dissertation is to cast light on the evolutionary history of tonal sounds by testing these hypotheses by combining comparative phylogenetic and field methods. This dissertation provides the first species-level phylogeny of Cetacea and phylogenetic tests of evolutionary hypotheses of cetacean communicative signals. Tonal sounds evolution is complex in that has likely been shaped by a combination of factors that may influence different aspects of their acoustical structure. At the inter-specific level, these results suggest that only tonal sound minimum frequency is constrained by body size. Group size also influences tonal sound minimum frequency. Species that live in large groups tend to produce higher frequency tonal sounds. The evolutionary history of tonal sounds and sociality may be intertwined, but in a complex manner rejecting simplistic views such as the hypothesis that tonal sounds evolved ‘for’ social communication in dolphins. Levels of social and tonal sound complexity nevertheless correlate indicating the importance of tonal sounds in social communication. At the intraspecific level, tonal sound variation in frequency and temporal parameters may be product of genetic isolation and local levels of underwater noise. This dissertation provides one of the first insights into the evolution of Cetacean tonal sounds in a phylogenetic context, and points out key species where future studies would be valuable to enrich our understanding of other factors also playing a role in tonal sound evolution. ^

Phylogenetic and Ecological Significance in the Evolution of Cetacean Tonal Sounds

Cetaceans are aquatic mammals that rely primarily on sound for most daily tasks. A compendium of sounds is emitted for orientation, prey detection, and predator avoidance, and to communicate. Communicative sounds are among the most studied Cetacean signals, particularly those referred to as tonal sounds. Because tonal sounds have been studied especially well in social dolphins, it has been assumed these sounds evolved as a social adaptation. However, whistles have been reported in ‘solitary’ species and have been secondarily lost three times in social lineages. Clearly, therefore, it is necessary to examine closely the association, if any, between whistles and sociality instead of merely assuming it. Several hypotheses have been proposed to explain the evolutionary history of Cetacean tonal sounds. The main goal of this dissertation is to cast light on the evolutionary history of tonal sounds by testing these hypotheses by combining comparative phylogenetic and field methods. This dissertation provides the first species-level phylogeny of Cetacea and phylogenetic tests of evolutionary hypotheses of cetacean communicative signals. Tonal sounds evolution is complex in that has likely been shaped by a combination of factors that may influence different aspects of their acoustical structure. At the inter-specific level, these results suggest that only tonal sound minimum frequency is constrained by body size. Group size also influences tonal sound minimum frequency. Species that live in large groups tend to produce higher frequency tonal sounds. The evolutionary history of tonal sounds and sociality may be intertwined, but in a complex manner rejecting simplistic views such as the hypothesis that tonal sounds evolved ‘for’ social communication in dolphins. Levels of social and tonal sound complexity nevertheless correlate indicating the importance of tonal sounds in social communication. At the intraspecific level, tonal sound variation in frequency and temporal parameters may be product of genetic isolation and local levels of underwater noise. This dissertation provides one of the first insights into the evolution of Cetacean tonal sounds in a phylogenetic context, and points out key species where future studies would be valuable to enrich our understanding of other factors also playing a role in tonal sound evolution.