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This paper introduces a time-varying threshold autoregressive model (TVTAR), which is used to examine the persistence of deviations from PPP. We find support for the stationary TVTAR against the unit root hypothesis; however, for some developing countries, we do not reject the TVTAR with a unit root in the corridor regime. We calculate magnitudes, frequencies, and durations of the deviations of exchange rates from forecasted changes in exchange rates. A key result is asymmetric adjustment. In developing countries, the average cumulative deviation from forecasts during periods when exchange rates are below forecasts is twice the corresponding measure during periods when exchange rates are above forecasts.
In this work, the physiological effects of time-varying magnetic fields up to 100 kHz have been investigated, namely magnetic stimulation and body warming. Simulation studies were based on numerical calculations on sophisticated cell and body models. In addition, magnetic stimulation thresholds have been determined experimentally.The project was carried out within the scope of the development of Magnetic Particle Imaging, a new imaging technology for medical diagnostics.
In the last two years or so, I was most fortunate in being given opportunities of lecturing on a new methodology to a variety of audiences in Britain, China, Finland, France and Spain. Despite my almost Confucian attitude of preferring talking (i.e. a transient record) to writing (i.e. a permanent record), the warm encouragement of friends has led to the ensuing notes. I am also only too conscious of the infancy of the methodology introduced in these notes. However, it is my sincere hope that exposure to a wider audience will accelerate its maturity. Readers are assumed to be familiar with the basic theory of time series analysis. The book by Professor M.B. Priestley (1981) may be used as a general reference. Chapter One is addressed to the general question: "why do we need non-linear time series models?" After describing some significant advantages of linear models, it singles out several major limitations of linearity. Of course, the selection reflects my personal view on the subject, which is only at its very beginning, although there does seem to be a general agreement in the literature that time irr'eversibility and limit cycles are among the most obvious.
We are confronted with emergent systems everywhere and Holland shows how a theory of emergence can predict many complex behaviours in art and science. This book will appeal to scientists and anyone interested in scientific theory.
A natural approach to survival analysis in many settings is to model the subject's "health'' status as a latent stochastic process, where the terminal event is represented by the first time that the process crosses a threshold. "Threshold regression'' models the covariate effects on the latent process. Much of the literature on threshold regression assumes that the process is a one-dimensional Wiener process, where crossing times have a tractable inverse Gaussian distribution but where the process characteristics are fixed at baseline. This framework is not easily extended to incorporate time-varying covariates or dependent competing risks. We introduce a novel approach for performing threshold regression with time-dependent covariates in a discrete time setting, where the process is a Gaussian random walk, with time-varying drift as a parameterized function of time-varying covariates. This model is then extended to consider dual correlated competing risks. We present methods for estimating model parameters, including an EM algorithm, and outline numerical algorithms for efficiently evaluating the observed and complete data likelihoods and score functions and for estimating standard errors. We discuss results of applying these methods to both simulated data and to the Freddie Mac residential mortgage data set. In the latter case we quantify associations between baseline borrower characteristics and time-varying macroeconomic conditions versus time to mortgage default and prepayment events.
This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology and communication or laser physics. Over the last decade, a number of new types of synchronization have been identified and some interesting new ideas concerning the synchronization have also appeared.This book presents the complete synchronization problem rather than just results from the research. The problem is demonstrated in relation to a kind of coupling applied between dynamical systems, whereby a unique classification of possible couplings is introduced. Another novel feature is the connection presented between synchronization and the problem of determining the Lyapunov exponents, especially for non-differentiable systems. A detailed proposal of such an estimation method and examples of its application are included.