Asymptotics for Fractional Processes

by James Davidson

Overview

Asymptotics for Fractional Processes develops an approach to the large-sample analysis of fractional partial-sum processes, featuring long memory increments. Long memory in a time series, equivalently called strong dependence, is usually defined to mean that the autocovariance sequence is non-summable. The processes studied have a linear moving average representation with a single parameter, denoted d, to measure the degree of long-run persistence. Long memory means that d is positive, while negative d defines a special type of short memory known as antipersistence in which the autocovariance sequence sums to zero. Antipersistent processes are treated in parallel with the long memory case. This book features the weak convergence of normalized partial sums to fractional Brownian motion and the limiting distribution of stochastic integrals where both the integrand and the integrator processes exhibit either long memory or antipersistence. It also covers applications to cointegration analysis and the treatment of dependent shock processes and includes chapters on the harmonic analysis of fractional models and local-to-unity autoregression.

Product Details

ISBN-13:	9780198955184
Publisher:	OUP Oxford
Publication date:	06/03/2025
Sold by:	Barnes & Noble
Format:	eBook
Pages:	224
File size:	993 KB

About the Author

James Davidson is Professor of Econometrics (Emeritus) at the University of Exeter. He graduated from the University of Birmingham in 1973 and received an MSc in Mathematical Economics and Econometrics from the London School of Economics and Political Science (LSE) in 1975. Since then, he has held teaching posts at the University of Warwick, LSE, the University of Wales Aberystwyth, Cardiff University, and the University of Exeter as well as visiting positions at the University of California Berkeley, the University of California San Diego, Hong Kong University of Science and Technology, and Central European University. Davidson is the author of Stochastic Limit Theory (Second Edition, 2021), Introduction to Econometric Theory (2018), and Econometric Theory (2000).

Table of Contents

1. The Fractional Model2. Fractional Asymptotics3. The FCLT for Fractional Processes4. The Fractional Covariance5. Stochastic Integrals6. Weak Convergence of Integrals7. Fractional Cointegration8. Autocorrelated Shocks9. Frequency Domain Analysis10. Autoregressive Roots near UnityA: Appendix: Useful ResultsB: Appendix: Identities and Integral SolutionsReferencesIndex