Time series models in non-normal situation: symmetric innovations (Q2742781)

The model under consideration is an \(AR(q)\) model of the type \(y_t=\sum_{j=1}^q \phi_jy_{t-j}+\varepsilon_t\), \(t=1,2,\dots,n\), where the innovations \(\{\varepsilon_t\}\) are i.i.d. r.v.s which have a distribution density NEWLINE\[NEWLINEf(x;p)=[\sigma\sqrt(k)\beta(1/2,p-1/2)]^{-1}(1+x^2/k\sigma^2)^{-p},\;-\infty<x<\infty,NEWLINE\]NEWLINE \(k=2p-3\), \(p\geq 2\), \(\beta(a,b)=\Gamma(a)\Gamma(b)/\Gamma(a+b)\). Since the maximum likelihood estimators are intractable in this case, the authors propose to use certain modified maximum likelihood estimators of the parameters such that the estimators are efficient. These estimators are also used for hypothesis testing and the resulting tests occurred to be robust and powerful.