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Estimation and testing stationarity for double-autoregressive models

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The paper considers the double-autoregressive model yt = yt−1+t with t = . Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln | +√αt|<0, which includes the cases with ||=1 or ||>1 as well as . It is well known that all kinds of estimators of in these cases are not normal when t 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.
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Keywords: Asymptotic normality; Brownian motion; Consistency; Double-autoregressive model; Lagrange multiplier test; Maximum likelihood estimator; Stationarity

Document Type: Research Article

Publication date: February 1, 2004

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