The Word was God: An Exegetical and Theological Survey of John 1:1

Graduate Textual or Investigativ

Fredholm inversion around a singularity: application to autoregressive time series in Banach space

This paper consider inverting a holomorphic Fredholm operator pencil. Specifically, we provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm operator pencil to have a simple pole and a second order pole. Based on those results, a closed-form expression of the Laurent expansion of the inverse around an isolated singularity is obtained in each case. As an application of the results, we obtain a suitable extension of the Granger-Johansen representation theory for random sequences taking values in a separable Banach space. Due to our closed-form expression of the inverse, we may fully characterize I(1) and I(2) solutions except a term that depends on initial values

Functional Principal Component Analysis of Cointegrated Functional Time Series

Functional principal component analysis (FPCA) has played an important role in the development of functional time series (FTS) analysis. This paper investigates how FPCA can be used to analyze cointegrated functional time series and propose a modification of FPCA as a novel statistical tool. Our modified FPCA not only provides an asymptotically more efficient estimator of the cointegrating vectors, but also leads to novel KPSS-type tests for examining some essential properties of cointegrated time series. As an empirical illustration, our methodology is applied to the time series of log-earning densities

Global Characteristics of the Correlation and Time Lag Between Solar and Ionospheric Parameters in the 27-day Period

The 27-day variations of topside ionosphere are investigated using the in-situ electron density measurements from the CHAMP planar Langmuir probe and GRACE K-band ranging system. As the two satellite systems orbit at the altitudes of approx. 370 km and approx. 480 km, respectively, the satellite data sets are greatly valuable for examining the electron density variations in the vicinity of F2-peak. In a 27-day period, the electron density measurements from the satellites are in good agreements with the solar flux, except during the solar minimum period. The time delays are mostly 1-2 day and represent the hemispherical asymmetry. The globally-estimated spatial patterns of the correlation between solar flux and in-situ satellite measurements show poor correlations in the (magnetic) equatorial region, which are not found from the ground measurements of vertically-integrated electron content. We suggest that the most plausible cause for the poor correlation is the vertical movement of ionization due to atmospheric dynamic processes that is not controlled by the solar extreme ultraviolet radiation