Read more
Long rangedependent, or long memory,time seriesarestationarytime series displaying a statistically signi?cant dependence between very distant obs- vations. We formalize this dependence by assuming that the autocorrelation function of these stationary series decays very slowly, hyperbolically, as a function of the time lag. Many economic series display these empirical features: volatility of asset prices returns, future interest rates, etc. There is a huge statistical literature on long memory processes, some of this research is highly technical, so that it is cited, but often misused in the applied econometrics and empirical e- nomics literature. The ?rst purpose of this book is to present in a formal and pedagogical way some statistical methods for studying long range dependent processes. Furthermore, the occurrence of long memory in economic time series might be a statistical artefact as the hyperbolic decay of the sample autoc- relation function does not necessarily derive from long range dependent p- cesses. Indeed, the realizations of non-homogeneous processes, e.g., switching regime and change point processes, display the same empirical features. We thus also present in this book recent statistical methods able to discriminate between the long memory and change point alternatives. Going beyond the purely statistical analysis of economic series, it is of interest to determine which economic mechanisms are generating the strong dependence properties of economic series, whether they are genuine, or spu- ous. The regularities of the long memory and change point properties across economic time series, e.g., common degree of long range dependence and/or common change points, suggest the existence of a common economic cause.
List of contents
Statistical Methods.- Recent Advances in ARCH Modelling.- Intermittency, Long-Memory and Financial Returns.- The Spectrum of Euro-Dollar.- Hölderian Invariance Principles and Some Applications for Testing Epidemic Changes.- Adaptive Detection of Multiple Change-Points in Asset Price Volatility.- Bandwidth Choice, Optimal Rates and Adaptivity in Semiparametric Estimation of Long Memory.- Wavelet Analysis of Nonlinear Long-Range Dependent Processes. Applications to Financial Time Series.- Prediction, Orthogonal Polynomials and Toeplitz Matrices. A Fast and Reliable Approximation to the Durbin-Levinson Algorithm.- Economic Models.- A Nonlinear Structural Model for Volatility Clustering.- Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models.- The Microeconomic Foundations of Instability in Financial Markets.- A Minimal Noise Trader Model with Realistic Time Series Properties.- Long Memory and Hysteresis.
Summary
A comprehensive survey on current and future developments in long memory analysis. The book assembles three different strands of long memory analysis: statistical literature – including tests – on the properties of LRD processes; mathematical literature on stochastic processes; and models from economic theory providing. The text is aimed at economists, econometricians, and statisticians interested in the study of long memory in economics.
