NEAR-INTEGRATED RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES

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+