a1 University of California, Davis
We determine the limiting behavior of near-integrated first-order random coefficient autoregressive RCA(1) time series. It is shown that the asymptotics of the finite-dimensional distributions crucially depends on how the critical value 1 is approached, which determines whether the process is near-stationary, has a unit root, or is mildly explosive. %In a second part, we derive the limit distribution of the serial correlation coefficient in the near stationary and the mildly explosive settings under very general conditions on the parameters. The results obtained are in accordance with those available for first-order autoregressive time series and can hence serve as an addition to existing literature in the area.
The author sincerely thanks the editor, P.C.B. Phillips, and two anonymous referees for a very careful reading of the manuscript, pointing out a series of flaws and mistakes, and providing simpler proofs. This has helped to prepare a much revised version of the original paper. This work was partially supported by NSF grant DMS-0604670, NSF-OTKA grant INT-0223262, and NATO grant PST.EAP.CLG 980599.