Clipped AR(p) with unknown threshold

Abstract

The present paper deals with a specific parameter estimation problem. Assuming a time series of 0-1-valued variables $\{X_n, n\in {\mathbb{N}}_0\}$ obtained by clipping a Gaussian AR(p) time series $\{Z_n, n\in {\mathbb{N}}_0\}$ at unknown threshold h, an efficient method for estimating parameters is proposed. If the number of observations is sufficient, the model proves to be highly accurate. A set of simulations is provided as an illustration of theoretical results, supporting the quality of the estimation.

Keywords:

• Clipped AR(p)
• Unknown threshold
• Parameters estimation

Notes

1 http://artax.karlin.mff.cuni.cz/∼flimmels/estimation_AR(p).r

Additional information

Funding

This work was supported by the grant F4/17/2017 (Robustnosť v úmyselnom useknutí časového radu), which has been provided by the Internal Grant Agency of the University of Economics in Prague.