A New Portmanteau Test for Short Memory in Long Memory Processes

• Activity Number: 514
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Timothy Hughes and Jaechoul Lee*+
• Companies: PacificSource and Boise State University
• Keywords: Asymptotic normal distribution ; ARFIMA ; Consistency ; Sample autocorrelations

Abstract

For a stationary autoregressive fractionally integrated moving-average process, it is often a priori known that the process involves long memory. However, if the long memory process has also short memory, existing methods are not satisfactory for identifying the short memory. This paper studies short memory characteristics in fractionally integrated long memory processes. Specifically, we propose a new portmanteau test that helps one determine if short memory components are statistically significant for the long memory time series. The proposed test attains target sizes and meets all favorable statistical properties, including the $\sqrt{n}$-convergence rate and the asymptotic normality for every value of the differencing parameter in fractionally integrated series. Our test is applied to actual time series data in economics and climatology.