Asymptotics for general nonstationary fractionally integratedprocesses without prehistoric influence

摘要

This paper derives a functional limit theorem for general nonstationaryfractionally integrated processes having no influence from prehistory. Asymptotic distributionsof sample autocovariances and sample autocorrelations based on these processesare also investigated. The problem arises naturally in discussing fractionally integratedprocesses when the processes starts at a given initial date.