Estimation and Testing Stationarity for Double-Autoregressive Models
- 22 December 2003
- journal article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 66 (1), 63-78
- https://doi.org/10.1111/j.1467-9868.2004.00432.x
Abstract
Summary: The paper considers the double-autoregressive model yt = φyt−1+ɛt with ɛt =ηt√(ω+αyt−12). Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln |φ +√αηt|1 as well as E(εt2)=∞. It is well known that all kinds of estimators of φ in these cases are not normal when ɛt are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for testing stationarity of the model and their asymptotic distributions are shown to be a function of bivariate Brownian motions. Critical values of the tests are tabulated and some simulation results are reported. An application to the US 90-day treasury bill rate series is given.Keywords
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