Double AR model without intercept: An alternative to modeling nonstationarity and heteroscedasticity |
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Authors: | Dong Li Shaojun Guo |
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Institution: | 1. Center for Statistical Science and Department of Industrial Engineering, Tsinghua University, Haidian District, Beijing, P.R. China;2. Institute of Statistics and Big Data, Renmin University of China, Haidian District, Beijing, P.R. China |
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Abstract: | This paper presents a double AR model without intercept (DARWIN model) and provides us a new way to study the nonstationary heteroscedastic time series. It is shown that the DARWIN model is always nonstationary and heteroscedastic, and its sample properties depend on the Lyapunov exponent. An easy-to-implement estimator is proposed for the Lyapunov exponent, and it is unbiased, strongly consistent, and asymptotically normal. Based on this estimator, a powerful test is constructed for testing the ordinary oscillation of the model. Moreover, this paper proposes the quasi-maximum likelihood estimator (QMLE) for the DARWIN model, which has an explicit form. The strong consistency and asymptotic normality of the QMLE are established regardless of the sign of the Lyapunov exponent. Simulation studies are conducted to assess the performance of the estimation and testing, and an empirical example is given for illustrating the usefulness of the DARWIN model. |
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Keywords: | DAR model DARWIN model geometric Brownian motion heteroscedasticity Lyapunov exponent nonstationary time series ordinary oscillation quasi-maximum likelihood estimation |
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