An exponential-squared estimator in the autoregressive model with heavy-tailed errors

In this paper, an exponential-squared estimator is introduced in the autoregressive model with heavy-tailed errors. Under some conditions, the $\sqrt{n}$-consistency of the proposed estimator is established. Since the exponential-squared estimator involves a tuning parameter $\lambda$, we select $\lambda$ via a fivefold cross validation procedure. Simulation studies illustrate that the finite sample performance of proposed method performs better than that of a self-weighted composite quantile regression (SWCQR) method and self-weighted least absolute deviation (SWLAD) method in terms of Sd and MSE when the error follows a heavy-tailed distribution and there are outliers in the dataset. Finally, we apply the proposed methodology to analyze the Recruitment series.

Keywords

autoregressive model, exponential squared loss, heavy-tailed distribution

2010 Mathematics Subject Classification

Primary 62G20. Secondary 62G35.

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Published 4 November 2015