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Estimation and testing stationarity for double‐autoregressive models
Author(s) -
Ling Shiqing
Publication year - 2004
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2004.00432.x
Subject(s) - autoregressive model , estimator , asymptotic distribution , mathematics , bivariate analysis , consistency (knowledge bases) , series (stratigraphy) , independent and identically distributed random variables , asymptotic analysis , statistics , econometrics , discrete mathematics , random variable , paleontology , biology
Summary. The paper considers the double‐autoregressive model y t = φ y t −1 + ɛ t with ɛ t =. Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln | φ +√ α η t |<0, which includes the cases with | φ |=1 or | φ |>1 as well as . It is well known that all kinds of estimators of φ in these cases are not normal when ɛ 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.