Asymptotics of M-estimators for moderate deviations from a unit root model with possibly infinite variance

Abstract

In this article, the M-estimator of the moderate deviations from a unit root model with possibly infinite variance errors is proposed. When the autoregressive coefficients are located on both sides of stationary and explosion, the asymptotic normal properties of the corresponding estimators for unknown parameters are proved, respectively. The asymptotic properties of the M-estimators are obtained in both the mildly integrated case and the mildly explosive case.

Keywords:

• Autoregressive model
• moderate deviations from a unit root model
• M-estimator
• infinite variance

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62F12

JEL CLASSIFICATION:

• C22

Acknowledgement

This research work is supported by National Natural Science Foundation of China (11901397, 71973098), Youth Academic Backbone Cultivation Project of Shanghai Normal University (310-AC7031-19-003021), General Research Fund of Shanghai Normal University (SK201720) and Key Subject of Quantitative Economics of Shanghai Normal University (310-AC7031-19-004221) and Academic Innovation Team of Shanghai Normal University (310-AC7031-19-004228).

Disclosure statement

The authors declare no conflict of interest.