Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

Thorium-230 coral chronology of a late prehistoric Hawaiian chiefdom

Documenting the history of settlement in Hawaii during the last few Centuries before European contact, is crucial to charting the evolution of the most complex chiefdom in Polynesia. It is precisely this period that Hawaii. and many Polynesian Societies, Underwent their most rapid changes in political, economic and social organisation. The last similar to 500 to 300 years in the C-14 calibration curve is problematic with wide fluctuations Often rendering large age spans that do not precisely date single events, especially troubling with a culture-historical record of similar to 1000 years duration. Here we present in extremely high precision Th-230 chronology for archaeologically constrained coral samples from a range of occupancy sites. Our high precision dates allow the time of site use to be clearly demonstrated. They also provide the first dates for habitation sites in Hawaii that clearly show contemporaneous occupation-the major problem in settlement pattern archaeology. We demonstrate that two sites were occupied within the same year. Our refined chronology, provides new and exciting oppurtunities for tracking sociopolitical and economic developments during the last few centuries-the crucial period in the evolution and transformation of Polynesian societies. (c) 2005 Elsevier Ltd. All rights reserved.