Iterated limits for aggregation of randomized INAR(1) processes with Poisson innovations

作者：Barczy Matyas^*; Nedenyi Fanni; Pap Gyula

来源：Journal of Mathematical Analysis and Applications, 2017, 451(1): 524-543.

DOI：10.1016/j.jmaa.2017.02.031

• Randomized INAR(1) process
• Temporal and contemporaneous aggregation
• Long memory
• Fractional Brownian motion
• Stable distribution
• Levy process

We discuss joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient alpha is an element of (0,1) and with idiosyncratic Poisson innovations. Assuming that a has a density function of the form psi(x)(1 - x)(beta), x is an element of (0,1), with lim(x up arrow 1)psi(x)=psi 1 is an element of (0, infinity), different limits of appropriately centered and scaled aggregated partial sums are shown to exist for beta is an element of (-1,0), beta=0, beta is an element of(0,1) or beta is an element of(1,8), when taking first the limit as N ->infinity and then the time scale n ->infinity, or vice versa. In fact, we give a partial solution to an open problem of Pilipauskaite and Surgailis [13] by replacing the random-coefficient AR(1) process with a certain randomized INAR(1) process.

• 出版日期2017-7-1