Abstract: |
This paper proposes a class of state-space models where the state equation is
a local-to-unity process. The large sample theory is obtained for the least
squares (LS) estimator of the autoregressive (AR) parameter in the AR
representation of the model under two sets of conditions. In the first set of
conditions, the error term in the observation equation is independent and
identically distributed (iid), and the error term in the state equation is
stationary and fractionally integrated with memory parameter H ϵ 2 (0; 1). It
is shown that both the rate of convergence and the asymptotic distribution of
the LS estimator depend on H. In the second set of conditions, the error term
in the observation equation is independent but not necessarily identically
distributed, and the error term in the state equation is strong mixing. When
both error terms are iid, we also develop the asymptotic theory for an
instrumental variable estimator. Special cases of our models are discussed. |