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. ^

Areal and vertical distribution of total soil mercury and total phosphorusin the southern half of water conservation area 3-A, Everglades, Southern Florida

Total soil-mercury and phosphorus concentrations were determined in 64 sites in the southern half of Water Conservation Area 3A, an area of approximately 500 km2 . Surface soil-Hg concentrations ranged from 117 to 300 ng-g-1;total phosphorus concentrations range from 350 to 850 pg~g-1. No consistent north-south or east-west trends are found in the mercury or phosphorus surface concentrations when they are normalized to soil bulk density. Nine sites were used for the determination of the vertical distribution of soilmercury. Vertical profiles of soil-Hg revealed decreasing concentrations with depth and correlated well with phosphorus in soil profiles. Mercury concentrations in soil profiles may be interpreted as an increase in the rate of deposition of mercury in the region in recent decades and/or as postdepositionalmobilization of mercury to surface layers.