NON-STATIONARITY AND QUASI-MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL
type="main" xml:id="jtsa12058-abs-0001"> <title type="main">Abstract</title>This article first studies the non-stationarity of the first-order double AR model, which is defined by the random recurrence equation <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" altimg="urn:x-wiley:01439782:media:jtsa12058:jtsa12058-math-0001" wiley:location="equation/jtsa12058-math-0001.gif"><msub><mrow><mi>y</mi></ mrow><mrow><mi>t</mi></mrow></msub><mo class="MathClass-rel">=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn>< /mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>t</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow></msub><mo class="MathClass-bin">+</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>t</mi>< /mrow></msub><msqrt><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>0</mn></m row></msub><mo class="MathClass-bin">+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn>< /mrow></msub><msubsup><mrow><mi>y</mi></mrow><mrow><mi>t</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msub sup></mrow></msqrt></math>, where γ<sub>0</sub> > 0, α<sub>0</sub> ≥ 0, and {η<sub>t</sub>}is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" altimg="urn:x-wiley:01439782:media:jtsa12058:jtsa12058-math-0002" wiley:location="equation/jtsa12058-math-0002.gif"><mi mathvariant="double-struck">E</mi><mi mathvariant="normal">log</mi><mo class="MathClass-rel">&7C</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn ></mrow></msub><mo class="MathClass-bin">+</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>t</mi>< /mrow></msub><msqrt><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></m row></msub></mrow></msqrt><mo class="MathClass-rel">&7C</mo><mo class="MathClass-rel">></mo><mn>0</mn></math>. Based on this, it is shown that the quasi-maximum likelihood estimator of (φ<sub>0</sub>,α<sub>0</sub>) is consistent and asymptotically normal so that the unit root problem does not exist in the double AR(1) model. Simulation studies are carried out to assess the performance of the quasi-maximum likelihood estimator in finite samples.
Year of publication: |
2014
|
---|---|
Authors: | Chen, Min ; Li, Dong ; Ling, Shiqing |
Published in: |
Journal of Time Series Analysis. - Wiley Blackwell, ISSN 0143-9782. - Vol. 35.2014, 3, p. 189-202
|
Publisher: |
Wiley Blackwell |
Saved in:
Online Resource
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