Asymptotics for Fractional Processes

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.