### Abstract

This paper develops the generalized empirical likelihood (GEL) method for infinite variance ARMA models, and constructs a robust testing procedure for general linear hypotheses. In particular, we use the GEL method based on the least absolute deviations and self-weighting, and construct a natural class of statistics including the empirical likelihood and the continuous updating-generalized method of moments for infinite variance ARMA models. The self-weighted GEL test statistic is shown to converge to a (Formula presented.)-distribution, although the model may have infinite variance. Therefore, we can make inference without estimating any unknown quantity of the model such as the tail index or the density function of unobserved innovation processes. We also compare the finite sample performance of the proposed test with the Wald-type test by Pan et al. (Econom Theory 23:852–879, 2007) via some simulation experiments.

Original language | English |
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Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Statistical Inference for Stochastic Processes |

DOIs | |

Publication status | Accepted/In press - 2017 Apr 9 |

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### Keywords

- Generalized empirical likelihood
- Heavy-tailed time series
- Infinite variance
- Linear hypothesis
- Self-weighted least absolute deviations

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models.** / Akashi, Fumiya.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Self-weighted generalized empirical likelihood methods for hypothesis testing in infinite variance ARMA models

AU - Akashi, Fumiya

PY - 2017/4/9

Y1 - 2017/4/9

N2 - This paper develops the generalized empirical likelihood (GEL) method for infinite variance ARMA models, and constructs a robust testing procedure for general linear hypotheses. In particular, we use the GEL method based on the least absolute deviations and self-weighting, and construct a natural class of statistics including the empirical likelihood and the continuous updating-generalized method of moments for infinite variance ARMA models. The self-weighted GEL test statistic is shown to converge to a (Formula presented.)-distribution, although the model may have infinite variance. Therefore, we can make inference without estimating any unknown quantity of the model such as the tail index or the density function of unobserved innovation processes. We also compare the finite sample performance of the proposed test with the Wald-type test by Pan et al. (Econom Theory 23:852–879, 2007) via some simulation experiments.

AB - This paper develops the generalized empirical likelihood (GEL) method for infinite variance ARMA models, and constructs a robust testing procedure for general linear hypotheses. In particular, we use the GEL method based on the least absolute deviations and self-weighting, and construct a natural class of statistics including the empirical likelihood and the continuous updating-generalized method of moments for infinite variance ARMA models. The self-weighted GEL test statistic is shown to converge to a (Formula presented.)-distribution, although the model may have infinite variance. Therefore, we can make inference without estimating any unknown quantity of the model such as the tail index or the density function of unobserved innovation processes. We also compare the finite sample performance of the proposed test with the Wald-type test by Pan et al. (Econom Theory 23:852–879, 2007) via some simulation experiments.

KW - Generalized empirical likelihood

KW - Heavy-tailed time series

KW - Infinite variance

KW - Linear hypothesis

KW - Self-weighted least absolute deviations

UR - http://www.scopus.com/inward/record.url?scp=85017105458&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85017105458&partnerID=8YFLogxK

U2 - 10.1007/s11203-017-9159-3

DO - 10.1007/s11203-017-9159-3

M3 - Article

AN - SCOPUS:85017105458

SP - 1

EP - 23

JO - Statistical Inference for Stochastic Processes

JF - Statistical Inference for Stochastic Processes

SN - 1387-0874

ER -