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.

The effects of varying time under tension and volume load on acute neuromuscular responses

The purpose of this study was to examine the effects of different methods of measuring training volume, controlled in different ways, on selected variables that reflect acute neuromuscular responses. Eighteen resistance-trained males performed three fatiguing protocols of dynamic constant external resistance exercise, involving elbow flexors, that manipulated either time-under-tension (TUT) or volume load (VL), defined as the product of training load and repetitions. Protocol A provided a standard for TUT and VL. Protocol B involved the same VL as Protocol A but only 40% concentric TUT; Protocol C was equated to Protocol A for TUT but only involved 50% VL. Fatigue was assessed by changes in maximum voluntary isometric contraction (MVIC), interpolated doublet (ID), muscle twitch characteristics (peak twitch, time to peak twitch, 0.5 relaxation time, and mean rates of force development and twitch relaxation). All protocols produced significant changes (P