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Theory and Method

Distribution of the Residual Cross-Correlation in Univariate ARMA Time Series Models

Pages 849-855 | Received 01 Mar 1977, Published online: 05 Apr 2012

References

  • Anderson , T. W. 1958 . An Introduction to Multivariate Statistical Analysis , New York : John Wiley & Sons .
  • Bartlett , M. S. 1966 . Stochastic Processes, , 2nd ed. , Cambridge , , England : Cambridge University Press .
  • Billingsley , Patrick . “The Lindeberg-Levy Theorem for Martingales” . Proceedings of the American Mathematical Society . Vol. 12 , pp. 788 – 792 .
  • Box , George E.P. and Jenkins , Gwilym M. 1970 . Time Series Analysis Forecasting and Control , San Francisco : Holden-Day .
  • Box , George E.P. , Jenkins , Gwilym M. and Pierce , David A. 1970 . “Distribution of the Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models” . Journal of the American Statistical Association , 65 : 1509 – 1526 .
  • Conveyou , R. R. and MacPherson , R. D. 1967 . “Fourier Analysis of Uniform Random Generators” . Journal of the Association of Computing Machinery , 14 : 100 – 119 .
  • Davies , N. , Triggs , C. M. and Newbold , P. 1977 . “Significance Levels of the Box-Pierce Portmanteau Statistic in Finite Samples” . Biometrika , 64 : 517 – 522 .
  • Durbin , James . 1970 . “Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors Are Lagged Dependent Variables” . Econometrica , 38 : 410 – 421 .
  • Fisher , R. A. 1921 . “Contribution to the Discussion of the Paper ‘On the Time-Correlation Problem,’ by G.U. Yule” . Journal of the Royal Statistical Society , 84 : 534 – 536 .
  • Granger , C. W.J. 1969 . “Investigating Causal Relations by Econometric Models and Cross-Spectral Methods” . Econometrica , 37 : 424 – 438 .
  • Haugh , Larry D. 1972a . “The Identification of Time Series Interrelationships With Special Reference to Dynamic Regression” , Madison : Dept. of Statistics, University of Wisconsin . unpublished PhD thesis
  • Haugh , Larry D. “Checking Time Series Interrelationships and Identifying Dynamic Regression Models for Short-Term Forecasting” . Proceedings of the American Statistical Association . pp. 325 – 330 . Business and Economic Statistics Section .
  • Haugh , Larry D. 1976 . “Checking the Independence of Two Covariance-Stationary Time Series: A Univariate Residual Cross-Correlation Approach” . Journal of the American Statistical Association , 71 : 378 – 385 .
  • Haugh , Larry D. and Box , George E.P. 1977 . “Identification of Dynamic Regression (Distributed Lag) Models Connecting Two Time Series” . Journal of the American Statistical Association , 72 : 121 – 130 .
  • Ljung , G. M. and Box , G. E.P. 1976 . “Maximum Likelihood Estimation in the Autoregressive Moving Average Model” , Madison : Dept. of Statistics, University of Wisconsin . Technical Report No. 476
  • Ljung , G. M. and Box , G. E.P. 1978 . “On a Measure of Lack of Fit in Time Series Models” . Biometrika , 65 : 297 – 303 .
  • Maindonald , J. H. 1976 . “Least Squares Programs—A Second Look” . The American Statistician , 30 : 202 – 203 .
  • Mann , Henry B. and Wald , Abraham . 1943 . “On Stochastic Limit and Order Relationships” . Annals of Mathematical Statistics , 14 : 217 – 226 .
  • Marsaglia , G. and Bray , T. A. 1964 . “A Convenient Method for Generating Normal Variables” . Society for Industrial and Applied Mathematics Review , 6 : 260 – 264 .
  • McLeod , Ian A. 1975 . “Derivation of the Theoretical Auto-covariance Function of Autoregressive-Moving Average Time Series” . Applied Statistics , 24 : 255 – 256 .
  • McLeod , Ian A. 1977a . “Topics in Time Series and Intervention Analysis” , Dept. of Statistics, University of Waterloo . unpublished PhD thesis
  • McLeod , Ian A. 1977b . “Improved Box-Jenkins Estimators” . Biometrika , 64 : 531 – 534 .
  • McLeod , Ian A. 1978 . “On the Distribution of Residual Autocorrelations in Box-Jenkins Models” . Journal of the Royal Statistical Society , 40 : 296 – 302 .
  • McLeod , Ian A. and Hipel , Keith W. 1978 . “Simulation Procedures for Box-Jenkins Models” . Water Resources Research , 14 : 969 – 975 .
  • Newbold , Paul . 1974 . “The Exact Likelihood Function for a Mixed Autoregressive-Moving Average Process” . Biometrika , 61 : 423 – 426 .
  • Pierce , David A. 1977a . “Relationships—and Lack Thereof—Between Economic Time Series, With Special Reference to Money and Interest Rates” . Journal of the American Statistical Association , 72 : 11 – 21 .
  • Pierce , David A. 1977b . R 2-Measures for Time Series” , Washington , D.C. : Federal Reserve Board . Special Studies Paper
  • Pierce , David A. and Haugh , Larry D. 1977 . “Causality in Temporal Systems: Characterizations and a Survey” . Journal of Econometrics , 5 : 265 – 293 .
  • Pierce , David A. and Haugh , Larry D. 1979 . “The Characterization of Instantaneous Causality: A Comment” . Journal of Econometrics , 10 : 257 – 259 .
  • Rao , C. R. 1974 . Linear Statistical Inference, , 2nd ed. , New York : John Wiley & Sons .

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