type="main" xml:id="jtsa12092-abs-0001"It is well known that estimating bilinear models is quite challenging. Many different ideas have been proposed to solve this problem. However, there is not a simple way to do inference even for its simple cases. This article proposes a generalized...

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>

We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X_k = (&phiv; + b_k)X_k - 1 + e_k, where (&phiv;, omega-super-2, σ-super-2) is the parameter of the process, , . We consider a nonstationary RCA process satisfying E log |&phiv; + b_0| = 0 and show that σ-super-2...

This paper obtains the joint limiting distribution of residuals and squared residuals of a general time-series model. Based on this, we propose a mixed portmanteau statistic for testing the adequacy of fitted time-series models. In some cases, it is shown that this statistic can be simply...