We investigate the nonstationary double <sc>ar(1)</sc> model, <disp-formula><graphic xlink:href="asm084ueq1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></disp-formula> where ω 0, α 0, the η_t are independent standard normal random variables and Elog |φ &plus; η_t√α| &ges; 0. We show that the maximum likelihood estimator of (φ, α) is consistent and asymptotically normal. Combination of this result with...

This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum...

This paper studies the least squares estimator (LSE) of the multiple-regime threshold autoregressive (TAR) model and establishes its asymptotic theory. It is shown that the LSE is strongly consistent. When the autoregressive function is discontinuous over each threshold, the estimated thresholds...

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 γ₀  0, α₀ ≥ 0, and {η_t}is a sequence of i.i.d. symmetric...<//msub></msubsup><//m></mrow><//></mrow>

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is <italic>n</italic>-consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the...

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(<italic>p</italic>, <italic>q</italic>) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of...