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Theory and Method

Testing for a Moving Average Unit Root in Autoregressive Integrated Moving Average Models

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Pages 596-601 | Received 01 Nov 1989, Published online: 27 Feb 2012

References

  • Ahtola , J. and Tiao , G. C. 1984 . Some Aspects of Parameter Inference for Nearly Nonstationary and Nearly Noninvertible ARMA Models II . Qüestiio , 8 : 155 – 163 .
  • Anderson , T. W. and Darling , D. A. 1952 . Asymptotic Theory of Certain “Goodness-of-Fit” Criteria Based on Stochastic Processes . The Annals of Mathematical Statistics , 23 : 193 – 212 .
  • Anderson , T. W. and Takemura , A. 1986 . Why Do Noninvertible Estimated Moving Averages Occur? . Journal of Time Series Analysis , 7 : 235 – 254 .
  • Ansley , C. F. 1979 . An Algorithm for the Exact Likelihood of a Mixed Autoregressive Moving Average Process . Biometrika , 66 : 547 – 553 .
  • Corbae , D. and Ouliaris , S. 1988 . Cointegration and Tests of Purchasing Power Parity . The Review of Economics and Statistics , 70 : 508 – 511 .
  • Cryer , J. D. and Ledolter , J. 1981 . Small Sample Properties of the Maximum Likelihood Estimator in the First-Order Moving Average Model . Biometrika , 68 : 691 – 696 .
  • Dent , W. 1977 . Computation of the Exact Likelihood Function of an ARIMA Process . Journal of Statistical Computation and Simulation , 5 : 193 – 206 .
  • Dickey , D. A. , Bell , W. R. and Miller , R. B. 1986 . Unit Roots in Time Series Models: Tests and Implications . American Statistician , 40 : 12 – 26 .
  • Engle , R. F. and Granger , C. W. J. 1987 . Cointegration and Error Correction: Representation, Estimation, and Testing . Econometrica , 55 : 251 – 276 .
  • Fuller , W. A. 1985 . “ Nonstationary Autoregressive Time Series ” . In Handbook of Statistics 5, Time Series in the Time Domain , Edited by: Hannan , E. J. , Krishnaiah , P. R. and Rao , M. M. 1 – 23 . Amsterdam : North-Holland .
  • Hannan , E. J. 1973 . The Asymptotic Theory of Linear Time Series Models . Journal of Applied Probability , 10 : 130 – 145 .
  • King , M. L. 1980 . Robust Tests for Spherical Symmetry and Their Application to Least Squares Regression . The Annals of Mathematical Statistics , 8 : 1265 – 1271 .
  • King , M. L. 1988 . Towards a Theory of Point Optimal Tests . Econometric Reviews , 6 : 169 – 218 .
  • King , M. L. and Hillier , G. H. 1985 . Locally Best Invariant Tests of the Error Covariance Matrix of the Linear Regression Model . Journal of the Royal Statistical Society , 47 : 98 – 102 . Ser. B
  • Kohn , R. 1978 . Asymptotic Properties of Time Domain Gaussian Estimators . Advances in Applied Probability , 10 : 339 – 359 .
  • Kohn , R. 1979 . Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models . Econometrica , 47 : 1005 – 1030 .
  • Nyblom , J. and Mäkeläinen , T. 1983 . Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model . Journal of the American Statistical Association , 78 : 856 – 864 .
  • Pesaran , M. H. 1983 . A Note on the Maximum Likelihood Estimation of Regression Models with First-Order Moving Average Errors with Roots on the Unit Circle . Australian Journal of Statistics , 25 : 442 – 448 .
  • Phillips , P. C. B. 1987 . Time Series Regression with a Unit Root . Econometrica , 55 : 277 – 301 .
  • Phillips , P. C. B. and Perron , P. 1988 . Testing for a Unit Root in Time Series Regression . Biometrika , 75 : 335 – 346 .
  • Said , S. E. and Dickey , D. A. 1985 . Hypothesis Testing in ARIMA (p, 1, q) Models . Journal of the American Statistical Association , 80 : 369 – 374 .
  • Sargan , J. D. and Bhargava , A. 1983 . Maximum Likelihood Estimation of Regression Models with First-Order Moving Average Errors when the Root Lies on the Unit Circle . Econometrica , 51 : 799 – 820 .
  • Schwert , G. W. 1989 . Tests for Unit Roots: A Monte Carlo Investigation . Journal of Business and Economic Statistics , 7 : 147 – 159 .
  • Shively , T. S. 1988 . An Exact Test for a Stochastic Coefficient in a Time Series Regression Model . Journal of Time Series Analysis , 9 : 81 – 88 .
  • Shively , T. S. , Ansley , C. F. and Kohn , R. 1990 . Fast Evaluation of the Distribution of the Durbin–Watson and Other Invariant Test Statistics in Time Series Regression . Journal of the American Statistical Association , 85 : 676 – 685 .
  • Tanaka , K. 1990 . Testing for a Moving Average Unit Root . Econometric Theory , 6 : 433 – 444 .
  • Tanaka , K. and Satchell , S. E. 1989 . Asymptotic Properties of the Maximum Likelihood and Nonlinear Least Squares Estimators for Noninvertible Moving Average Models . Econometric Theory , 5 : 333 – 353 .

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