Aggregation of autoregressive processes and long memory

• DOI: 10.48550/arxiv.0811.1917
• Publication Date: 2008-01-01
• Authors: Didier Dacunha‐Ca...; Lisandro Fermín
• Keywords: 60G50; 60G10; 60G50; 62M10; 91B84; Probability (math.PR); Mathematics - Statistics Theory; Statistics Theory (math.ST); 01 natural sciences; 91B84; FOS: Mathematics; 62M10; 0101 mathematics; 60G10; Mathematics - Probability

We study the aggregation of AR processes and generalized Ornstein-Uhlenbeck (OU) processes. Mixture spectral densities with random poles are main tool. In this context, we apply our results for doubly stochastic interactives processes, see Dacunha-Castelle Fermin (2006). Thus, relationship between autoregressive long memory considering complex interaction structures. precise a very interesting qualitative phenomena: how creation depends on concentration near to boundary stability (measured in Prokhorov sense). Our extends given by Oppenheim Viano (2004), highlight importance angular dispersion measure appearance memory.