Journal
JOURNAL OF ECONOMETRICS
Volume 215, Issue 1, Pages 165-183Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2019.08.009
Keywords
Augmented DAR model; DAR model; Heavy-tailedness; Non-standard asymptotics; Parameter on the boundary; Portmanteau test; Self-weighted QMLE
Categories
Funding
- NSFC [11571348, 11690014, 11731015, 71532013, 71973077, 11771239]
- Tsinghua University Initiative Scientific Research Program [2019Z07L01009]
- RGC of Hong Kong [17306818, 17305619]
- Seed Fund for Basic Research [201611159233, 201811159049]
- Hung Hing Ying Physical Sciences Research Fund [2017-18]
- Fundamental Research Funds for the Central University [19JNYH08]
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This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows the applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data are stationary, and its usefulness is illustrated by simulation studies and one real example. (C) 2019 Elsevier B.V. All rights reserved.
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