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. ^

The moderate voice of John Sherman and the Republican agenda 1855-1898

Republican John Sherman, United States Congressman, Senator, Treasury Secretary, and Secretary of State had a political career of major importance from 1855 to 1898, yet there have been only casual references by historians and only two biographies of him, with the most recent published in 1902. From a strong Whig Party background, he was first elected to the United States House of Representatives in 1854; switching to the Republicans that same year. Then elevated to the Senate in 1861, he served in that body throughout the Civil War and Reconstruction when he was the most important voice of party unity and moderation. In 1877, the new President Rutherford Hayes appointed Sherman Secretary of the Treasury. He returned to the Senate after the Hayes administration where he sat for the following 15 years. In this particularly notable period, he not only led the upper house, but he engineered more bills in Congress which bore his name than any other member of either house. These included the critically important Sherman Silver Purchase Act, the Sherman Anti-Trust Act and Sherman Inter-State Commerce Act. In 1897 he left the Senate finally when William McKinley appointed him Secretary of State. ^ Through this long, distinguished career, Sherman was involved in all the important legislation that brought the country through the Civil War and Reconstruction and into the post-war world of the Gilded Age of rapid industrialization, and urban growth, Politically, he never strayed far from the nationalistic and economic principles of the Whig Party, and brought both these values to bear in the Republican Party that dominated American political life from 1860 to 1900. Similarly, party loyalty and loyalty to the President always characterized his service. He was indeed, an exemplar of political and statesmanship. ^ While research for this dissertation included review of both journal and monographic literature, its basis lies more critically in primary research in unpublished archival material in repositories from Maine to Ohio, in particular the Library of Congress. ^