Joint aggregation of random-coefficient AR(1) processes with common innovations

Abstract

We discuss joint temporal and contemporaneous aggregation of N copies of stationary random-coefficient AR(1) processes with common i.i.d. standardized innovations, when N and time scale n increase at different rate. Assuming that the random coefficient a has a density, regularly varying at a=1 with exponent −1/2<β<0, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+β)/n tends to (i) ∞, (ii) 0, (iii) 0<μ<∞. The paper extends the results in Pilipauskaitė and Surgailis (2014) from the case of idiosyncratic innovations to the case of common innovations.