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. ^

Broadband RF current detector

The problems to be solved in this thesis were 1) development of a broadband RF preamplifier to be used with non-ferrous current probes so that the amplified signal exceeds the errors due to cable pickup, no detection is needed in this application, and 2) development of a self-contained device that amplifies and detects the output from a nonferrous current probe, providing a digital readout of the current. These instruments have been completed and are being tested for use by the National Institutes of Occupational Safety and Health (NIOSH). The self-contained current meter operates at frequencies up to 600 MHz, and detects currents as low as 8 mA . At these current magnitudes, the probe (pick-up coil) will output a voltage of 500μV (-53 dBm on 50Ω) which will have to be raised above 0 dBm. The final circuit uses a RF mixer as a variable attenuator in order to increase the dynamic range, two Monolithic Microwave Integrated Circuits (MMIC) for preamplification, a final broadband amplifier to raise the output compression point, a Schottky diode detector, a sample and hold circuit, and a liquid crystal digital panel meter.