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

Fumiya Akashi

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1-23
Number of pages23
JournalStatistical Inference for Stochastic Processes
DOIs
Publication statusAccepted/In press - 2017 Apr 9

Fingerprint

Infinite Variance
ARMA Model
Empirical Likelihood
Likelihood Methods
Hypothesis Testing
Linear Hypothesis
Tail Index
Least Absolute Deviation
Generalized Method of Moments
Density Function
Simulation Experiment
Test Statistic
Weighting
Updating
Statistics
Converge
Unknown
Testing
Model

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

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