Long Memory and Aggregation

• Activity Number: 657
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Donatas Surgailis*+
• Companies: Vilnius University
• Keywords: contemporaneous aggregation ; autoregressive random field ; anisotropic long memory ; mixed stable moving average ; operator self-similarity

Abstract

The idea of aggregating random coefficient short memory dynamics (e.g., AR(1)) to define long memory process goes back to Granger (1980). This talk will concentrate on aggregation of nearest neighbor autoregressive random fields on two-dimensional lattice with random coefficient having a regularly varying probability density near the unit root. Depending on the form of the autoregressive operator, the aggregated random field is shown to exhibit isotropic or anisotropic long memory, the latter being characterized by the scaling behavior of partial sums on incommensurate rectangles with sides growing at different rates.