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Original Articles

Using the Residual White Noise Autoregressive Order Determination Criterion to Identify Unit Roots in Arima Models

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Pages 259-293 | Received 01 Dec 1997, Published online: 27 Jun 2007

References

  • Abraham , B and Ledolter , J. 1983 . “ Statistical Methods for Forecasting ” . New York : John Wiley and Sons .
  • Beguin , J.M. , Gourieroux , C. and Montfort , A. 1980 . “ Identification of Mixed Autoregressive-Moving Average Process: The Corner Method ” . In Time Series Edited by: Anderson , O. D. 423 – 436 . Amsterdam, , North Holland
  • Bhansali , R.J. 1991 . Consistent Recursive Estimation of the Order of an Autoregressive Moving Average Process . International Statistics Review , 59 : 81 – 96 .
  • Box , G.E.P. and Jenkins , G.M. 1976 . Time Series Analysis Forecasting and Control , San Francisco : Holden-Day .
  • Box , G.E.P and Pierce , D.A. 1970 . Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models . Journal of the American Statistical Association , 65 : 1509 – 1526 .
  • Burg , J.P. 1975 . “ Maximal Entropy Spectral Analysis ” . In Dept. of Geophysics , Stanford University . Ph.D. dissertation
  • Coen , P. , Gomme , E. and Kendall , M. 1969 . Lagged Relationship in Economic Forecasting (with discussion) . Journal of the Royal Statistical Society , A 135 : 133 – 163 .
  • Dickey , D. , Bell , W. and Miller , R. 1986 . Unit-Roots in Time Series Models: Tests and Implications . The American Statistician , 40 : 12 – 26 .
  • Dickey , D. and Fuller , W. 1979 . Distribution of the Estimators for Autoregressive Time Series with a Unit Root . Journal of the American Statistical Association , 74 : 427 – 431 .
  • Dickey , D. and Fuller , W. 1981 . Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root . Econometrica , 49 : 1057 – 1072 .
  • Fuller , W. 1976 . Introduction to Statistical Time Series , New York : Wiley .
  • Hannan , E.J. 1980 . The Estimation of the Order of an ARMA Process . Annals of Statistics , 8 : 1071 – 1081 .
  • Hannan , E.J. and Kavalieris , L. 1984 . A Method for Autoregressive-Moving Average Estimation . Biometrika , 71 : 273 – 280 .
  • Kallinen , A. and Pukkila , T. 1991 . “ The Cholesky Decomposition of the Autocovariance Matrix.” in A Spectrum of Statistical Thought ” . In Essays in Statistical Theory, Economics and Population Genetics in Honour of Johan Fellman , Edited by: Rosenqvist , J.G. , Norstrom , K. and Palmgren , J. Vol. 46 , 113 – 124 . Helsinki, , Finland : Swedish School of Economics and Business Administration .
  • Kavalieris , L. , Hannan , E. and Salau , M. 1993 . “ The Estimation of ARMA Models: Some Comments ” . Australian National University . Department of Statistics Working Paper
  • Koreisha , S. and Pukkila , T. 1990 . A Generalized Least Squares Approach for Estimation of Autoregressive Moving Average Modhels . Journal Time Series Analysis , 11 : 139 – 151 .
  • Koreisha , S. and Yoshimoto , G. 1991 . A Comparison among Identification Procedures for Autoregressive Moving Average Models . International Statistics Review , 59 : 37 – 57 .
  • Koreisha , S. and Pukkila , T. 1993 . New Approaches for Determining the Degree of Differencing Necessary to Induce Stationarity in ARIMA Models . Journal of Statistical Planning and Inference , 36 : 399 – 412 .
  • Koreisha , S. and Pukkila , T. 1993 . Determining the Order of a Vector Autoregression When the Number of Component Series Is Large . Journal of Time Series Analysis , 14 : 47 – 69 .
  • Ljung , G. and Box , G.E.P. 1978 . On a Measure of Lack of Fit in Time Series Models . Biometrika , 65 : 297 – 303 .
  • Newbold , P. and Bos , T. 1990 . Introductory Business Forecasting , Cincinnati, Ohio : Southwestern .
  • Nelson , C. and Plosser , C. 1982 . Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications . Journal of Monetary Economics , 10 : 139 – 162 .
  • Phillips , P . 1987 . Time Series Regression with a Unit Root . Econometrica , 55 : 277 – 301 .
  • Phillips , P. and Perron , P. 1988 . Testing for a Unit Root in Time Series Regression . Biometrika , 75 : 335 – 346 .
  • Phillips , P. and Ploberger , W. 1994 . Posterior Odds Testing for a Selected Unit Root with Data-Based Model Selection . Econometric Theory , 10 : 774 – 808 .
  • Poskitt , D. and Salau , M. 1995 . On the Relationship Between Generalized Least Squares and Gaussian Estimation of Vector ARMA Models . Journal of Time Series Analysis , 16 : 617 – 645 .
  • Pukkila , T. , Koreisha , S. and Kallinen , A. 1990 . The Identification of ARMA Models . Biometrika , 77 : 537 – 548 .
  • Said , S. and Dickey , D. 1984 . Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order . Biometrika , 71 : 599 – 607 .
  • Said , S. and Dickey , D. 1985 . Hypothesis Testing in ARIMA(p,l,q) Models . Journal of the American Statistical Association , 80 : 369 – 374 .
  • Schwert , G. 1989 . Test for Unit Roots: A Monte Carlo Investigation . Journal of Business and Economic Statistics , 7 : 147 – 159 .
  • Stock , J. 1994 . Deciding between I(1) and I(0) . Journal of Econometrics , 63 : 105 – 131 .
  • Tiao , G. and Box , G. 1981 . Modeling Multiple Time Series With Applications . Journal of the American Statistical Association , 75 : 802 – 816 .
  • Tiao , G. and Tsay , R. 1984 . Consistency Properties of Least Squares Estimates of Autoregressive Parameters in ARMA Models . Annals of Statistics , 11 : 599 – 607 .
  • Tsay , R.S. and Tiao , G.C. 1984 . Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models . Journal of the American Statistical Association , 79 : 84 – 96 .

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