A SIMPLE EXAMPLE OF AN INDIRECT ESTIMATOR WITH DISCONTINUOUS LIMIT THEORY IN THE MA(1) MODEL

作者：Arvanitis Stelios^*

来源：Journal of Time Series Analysis, 2014, 35(6): 536-557.

DOI：10.1111/jtsa.12080

• Indirect estimator
• binding function
• indirect identification
• MA (1) process
• multiplicative structure
• martingale difference CLT
• CLT to stochastic integrals
• sequence of local alternatives
• rate of convergence dependent on the parameter
• discontinuous weak limits
• non-regularity

Indirect estimators usually emerge from two-step optimization procedures. Each step in such a procedure may induce complexities in the asymptotic theory of the estimator. In this note, we are occupied with a simple example in which the estimator defined by the inversion of the binding function has a discontinuous' limit theory even in cases where the auxiliary one does not. This example lives in the framework of estimation of the MA (1) parameter. The discontinuities' involve the dependence of the rate of convergence on the parameter, the non-continuity of the limit distribution w.r.t. the parameter and the estimator's non-regularity. We are also occupied with a more complex example where the discontinuities occur because of complexities induced in any step of the defining procedure. We present some Monte Carlo evidence on the quality of the approximations from the limit distributions.

• 出版日期2014-11