A casual VARMA model analysis with an application to Canadian money and income data

References

• Akaike , H. 1969 . Fitting autoregressions for prediction . Annals of the Institute of Statistical Mathematics , 21 : 243 – 247 .
   Web of Science ®Google Scholar
• Bartlett , M. S. 1946 . On the theoretival specification and sampling properties of autocorrelated time series . Journal of the Royal Statistical Society, Supplement , 8 : 27 – 41 .
   Google Scholar
• Berndt , E. and Savin , N. E. 1977 . Conflict among criteria for testing hypotheses in the multivariate linear regression model . Econometrica , 45 : 1263 – 1278 .
   Web of Science ®Google Scholar
• Box , G. E. P. and Jenkins , G. M. 1976 . Time Series Analysis: Forecasting and Control , 2nd edn , San Francisco : Holden-Day .
   Google Scholar
• Chowdhury , A. R. 1987 . Are causal relationships sensitive to causality tests? . Applied Economics , 19 : 459 – 465 .
   Web of Science ®Google Scholar
• Eberts , R. W. and Steece , B. M. 1984 . A test for Granger-causality in a multivariate ARMA model . Empirical Economics , 9 : 51 – 58 .
   Google Scholar
• Fackler , J. S. and Krieger , S. C. 1986 . An application of vector time series techniques to macroeconomic forecasting . Journal of Business and Economic Statistics , 4 : 71 – 80 .
   Web of Science ®Google Scholar
• Feige , E. L. and Pearce , D. K. 1979 . The casual relationship between money and income: some caveats for time series analysis . Review of Economics and Statistics , 61 : 521 – 533 .
   Web of Science ®Google Scholar
• Granger , C. W. J. 1969 . Investigating causal relations by econometric and cross-spectral models . Econometrica , 37 : 424 – 439 .
   Web of Science ®Google Scholar
• Hillmer , S. C. and Tiao , G. C. 1979 . Likelihood function of stationary multiple autoregressive moving average models . Journal of the American Statistical Association , 74 : 652 – 660 .
   Web of Science ®Google Scholar
• Hosking , J. R. M. 1980 . The multivarite portmanteau statistic . Journal of the American Statistical Association , 75 : 602 – 607 .
   Web of Science ®Google Scholar
• Hsiao , C. 1979 . Autoregressive modeling of canadian money and income data . Journal of the American Statistical Association , 74 : 553 – 560 .
   Web of Science ®Google Scholar
• Hsiao , C. 1981 . Autoregresive modeling and money-income causality detection . Journal of Monetary Economics , 7 : 85 – 106 .
   Web of Science ®Google Scholar
• Hsiao , C. 1982 . Autoregressive modeling and causal ordering of economic variables . Journal of Economic Dynamics and Control , 4 : 234 – 259 .
   Web of Science ®Google Scholar
• Hundley , G. and Koreisha , S. 1987 . The specification of econometric strike models: a VARMA approach . Applied Economics , 19 : 511 – 530 .
   Web of Science ®Google Scholar
• James , C. , Koreisha , S. and Partch , M. 1985 . A VARMA analysis of the causal relations among stock returns, real output, and nominal interest rates . The Journal of Finance , 40 : 1375 – 1384 .
   Web of Science ®Google Scholar
• Kang , H. 1981 . Necessary and sufficient condition for causality testing in multivariate ARMA models . Journal of Times Series Analysis , 2 : 95 – 101 .
   Google Scholar
• Li , W. K. and McLeod , A. I. 1981 . Distribution of the residual autocorrelation in multivariate ARMA times series models . Journal of the Royal Statistical Society , 43 : 231 – 239 . Ser B
   Google Scholar
• Nakhaeizadeh , G. 1987 . The causality direction in consumption-income process and sensitivity to lag structures . Applied Economics , 19 : 829 – 838 .
   Web of Science ®Google Scholar
• Newbold , P. 1983 . ARIMA model building and the time series analysis approach to forecasting . Journal of Forecasting , 2 : 23 – 35 .
   Web of Science ®Google Scholar
• Newbold , P. and Hotopp , S. M. 1986 . Testing causality using efficiently parametrized vector ARMA models . Applied Mathematics and Computation , 20 : 329 – 348 .
   Web of Science ®Google Scholar
• Roberts , D. L. and Nord , S. 1985 . Causality tests and functional form sensitivity . Applied Economics , 17 : 135 – 141 .
   Web of Science ®Google Scholar
• Savin , N. E. 1976 . Conflict among testing procedures in linear regression model with autoregressive disturbances . Econometrica , 44 : 1303 – 1315 .
   Web of Science ®Google Scholar
• Schwert , G. W. 1979 . “ The message in the innovations ” . In Three Aspects of Policy and Policymaking: Knowledge, Data and Institutions , Edited by: Brunner , K. and Meltzer , A. 9 – 54 . Amsterdam : North-Holland . Carnegie-Rochester Conference Series (Vol. 10)
   Google Scholar
• Sims , C. A. 1972 . Money, income and causality . American Economic Review , 62 : 540 – 555 .
   Web of Science ®Google Scholar
• Sims , C. A. 1980 . Macroeconomics and reality . Econometrica , 48 : 1 – 48 .
   Web of Science ®Google Scholar
• Spliid , H. 1983 . A Fast estimation method for the vector autoregressive moving average model with exogenous variables . Journal of the American Statistical Association , 78 : 843 – 849 .
   Web of Science ®Google Scholar
• Tiao , G. C. and Box , G. E. P. 1981 . Modeling multiple time series with applications . Journal of the American Statistical Association , 76 : 802 – 816 .
   Web of Science ®Google Scholar
• Tiao , G. C. and Tsay , R. S. 1983 . Multiple time series modeling and extended sample crosscorrelations . Journal of Business and Economic Statistics , 1 : 43 – 56 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Wallis , K. F. 1977 . Multiple time series analysis and the final form of econometric models . Econometrica , 45 : 1481 – 1497 .
   Web of Science ®Google Scholar
• Zellner , A. 1979a . Statistical analysis of econometric models . Journal of the American Statistical Association , 74 : 628 – 643 .
   Web of Science ®Google Scholar
• Zellner , A. 1979b . “ Causality in econometrics ” . In Three Aspects of Policy and Policymaking: Knowledge, Data and Institutions , Edited by: Brunner , K. and Meltzer , A. 9 – 54 . Amsterdam : North-Holland . Carnegie-Rochester Conference Series (Vol. 10)
   Google Scholar
• Zellner , A. 1984 . Basic Issues in Econometrics , Chicago : The University of Chicago Press .
   Google Scholar