Abstract :
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+
