Factor double autoregressive models with application to simultaneous causality testing

•This paper proposes a FDAR model, which captures both the causality-in-mean and causality-in-variance together.•A score test is investigated to test the causality-in-mean and causality-in-variance, simultaneously.•The QMLE is also considered for the FDAR model, and its strong consistency and asymptotical normality are studied.

Testing causality-in-mean and causality-in-variance has been largely studied. However, none of the tests can detect causality-in-mean and causality-in-variance simultaneously. In this paper, we introduce a factor double autoregressive (FDAR) model. Based on this model, a score test is proposed to detect causality-in-mean and causality-in-variance simultaneously. Furthermore, strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for the FDAR model are established. A small simulation study shows good performances of the QMLE and the score test in finite samples. A real data example on the causal relationship between Hong Kong stock market and US stock market is given.