Sparse Autoregressive based Estimation for Long-memory Models

摘要

Many economic, financial and engineering time series data exhibit long-term persistence. The autoregressive fractionally integrated moving average (ARFIMA) process is characterized by a slowly decaying autocorrelation function and arises as a popular statistical tool for modeling long memory time series. After years of development on the semipara-metric two-stage direct estimation of ARFIMA, recently there has been a considerable interest in the long-order autoregressive (AR) approximation, as it is observed to be simple and effective. This paper proposes a sparse AR approximation to the ARFIMA process based on penalized conditional likelihood. Simulation study shows that the proposed method leads to better model flexibility and prediction accuracy. Finally, we apply the method to analyze a foreign exchange rate data and the result is very satisfactory.