Mildly Explosive Autoregression with Strong Mixing Errors.

Area of Science:

• Time Series Analysis
• Econometrics
• Statistical Inference

Background:

• Autoregressive models are fundamental in time series analysis.
• Mildly explosive autoregression presents unique statistical challenges.
• Understanding error structures, like α-mixing, is crucial for robust estimation.

Purpose of the Study:

• To establish the limiting distribution for the least squares estimator in mildly explosive autoregressive models with α-mixing errors.
• To extend existing results for independent and geometrically α-mixing errors.
• To validate the theoretical findings through simulations and real-world data application.

Main Methods:

• Consideration of a mildly explosive autoregression model: yt=ρnyt−1+ut.
• Analysis under weak conditions including zero mean, finite fourth moment of errors, and specific mixing coefficients.
• Derivation of the Cauchy limiting distribution for the least squares estimator (ρ^n).

Main Results:

• The Cauchy limiting distribution is established for the least squares estimator (ρ^n) under α-mixing errors.
• This result generalizes previous findings for independent and geometrically α-mixing errors.
• Simulations demonstrate good finite sample performance of the derived distribution.

Conclusions:

• The study provides a robust theoretical framework for analyzing mildly explosive autoregressive processes with dependent errors.
• The established Cauchy limiting distribution offers a valuable tool for statistical inference in such models.
• The methodology is applied to real financial data, showcasing its practical relevance.