Skip to main content
SpringerLink
Log in

A comparison of classical tests of criterion when determining Granger causality with a bivariate ARMA model

  • Published:
Empirical Economics Aims and scope Submit manuscript

Abstract

The necessary and sufficient conditions for determining Granger causality with a bivariate ARMA model have been presented by Granger (1969), Haugh and Pierce (1977) and Eberts and Steece (1984). However the literature fails to address the question as to which classical test criterion likelihood ratio, Lagrange multiplier, Rao efficient scoring or Wald should be employed. This study addresses this question via a simulation study.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aitchson J, Silvey SD (1958) Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics 29:813–828

    Google Scholar 

  • Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Statist Math 21:243–247

    Google Scholar 

  • Bera AK, Byron RP, Jarque CM (1981) Further evidence in asymptotic tests for homogeneity and symmetry in large demand systems. Economics Letters 8:101–105

    Article  Google Scholar 

  • Berndt ER, Savin NE (1977) Conflict among criteria for testing hypotheses in the multivariate linear regression model. Econometrica 45:1263–1277

    Google Scholar 

  • Box GEP, Tiao G (1979) An introduction to applied multiple time series analysis. Technical Report #582, Department of Statistics, University of Wisconsin-Madison

  • Breusch TS, Pagan AR (1980) The Lagrange multiplier test and its applications to model specification in econometrics. Review of Economic Studies 47:239–253

    Google Scholar 

  • Buse A (1982) The likelihood ratio, Wald and Lagrange multiplier tests: an expository note. The American Statistician 36:153–157

    Google Scholar 

  • Eberts RW, Steece B (1984) A test for Granger causality in a multivariate ARMA model. Empirical Economics 9:51–58

    Article  Google Scholar 

  • Evans GBA, Savin NE (1982) Conflict among the criteria revisited: the W, LR, and LM tests. Econometrica 50:737–748

    Google Scholar 

  • Feige FL, Pearce DK (1979) The casual causal relationship between money and income; some caveats for time series analysis. Review of Economics and Statistics 61:521–533

    Google Scholar 

  • Granger CWJ (1969) Investigating causal relationships by econometric and cross-spectral models. Econometrica 37:424–438

    Google Scholar 

  • Granger CWJ, Newbold P (1977) Forecasting economic time series. Academic Press, New York

    Google Scholar 

  • Hannan EJ, Quinn E (1979) The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B 41/2:190–195

    Google Scholar 

  • Hannan EJ (1980) The estimation of the order of an ARMA process. The Annals of Statistics 8/5:1071–1081

    Google Scholar 

  • Harvey AC (1981) The econometric analysis of time series. Halstead Press, John Wiley & Sons, Inc., New York

    Google Scholar 

  • Haugh L, Pierce DA (1977) Causality in temporal systems: characterizations and a survey. Journal of Econometrics 5:265–293

    Article  Google Scholar 

  • Hillmer SC, Tiao GC (1979) Likelihood function of stationary multiple autoregressive moving average models. Journal of the American Statistical Association 74:652–660

    Google Scholar 

  • Hogg RV, Craig AT (1970) Introduction to mathematical statistics, 3rd ed. Macmillan Publishing Co., Inc., New York

    Google Scholar 

  • Hosking JRM (1980) Lagrange-multiplier tests of time series models. Journal of the Royal Statistical Society, Series B 42:170–181

    Google Scholar 

  • IMSL Computer package (1982) 9th ed. 7500 Bellaue Boulevard, Houston, TX 70036

  • Jeffreys H (1961) Theory of probability, 3rd ed. Clarendon, Oxford

    Google Scholar 

  • Judge GG, Griffiths WE, Lee RC, Lee TC (1980) The theory and practice of econometrics. John Wiley and Sons, Inc., New York

    Google Scholar 

  • Koreisha SG (1983) The relationship between transfer functions. Journal of forecasting 2:151–168

    Google Scholar 

  • Koreisha SG (1984) Estimation and forecasting of equations with expectations variables using multiple input transfer functions. In: Anderson OD (ed) Applied time series analysis II

  • Laitinen K (1978) Why is demand homogeneity so often rejected? Economics Letters 1:187–191

    Article  Google Scholar 

  • Meisner JF (1979) The sad fate of the asymptotic Slutsky symmetry test for large systems. Economics Letters 2:231–233

    Article  Google Scholar 

  • Nelson C (1979) Discussion of the Zellner and Schwert papers. Carnegie-Rochester Conference Series on Public Policy (supplement to Journal of Monetary Economics) 10:97–101

    Article  Google Scholar 

  • Nelson C, Schwert G (1982) Tests for predictive relationship between time series variables: Monte Carlo investigation. Journal of American Statistical Association 77:11–18

    Google Scholar 

  • Pierce DA (1977) Relationships — and the lack therefore — between economic time series, with special reference to money and interest rates. Journal of the American Statistical Association 72:11–26

    Google Scholar 

  • Poskitt DS, Tremayne AR (1982) Diagnostic tests for multiple time series models. The Annals of Statistics 10:114–120

    Google Scholar 

  • Quenouille MH (1957) The analysis of multiple time series. Griffin, London

    Google Scholar 

  • Rao CR (1973) Linear statistical inference and its application, 2nd ed. Wiley, New York

    Google Scholar 

  • Sargent TJ (1976) A classical econometric model of the United States. Journal of Political Economy 84:207–237

    Article  Google Scholar 

  • Savin NE (1976) Conflict among testing procedures in a linear regression model with autoregressive disturbances. Econometrica 44:1303–1315

    Google Scholar 

  • Schwartz G (1978) Estimating the dimension of a model. Annals of Statistics 6/2:461–464

    Google Scholar 

  • Schwert G (1979) Tests of causality; the message in the innovation. Carnegie-Rochester Conference Series on Public Policy (supplement to Journal of Monetary Economics) 10:55–96

    Google Scholar 

  • Silvey SD (1959) Lagrangian multiplier test. Annals of Mathematical Statistics 30:389–407

    Google Scholar 

  • Sims CA (1972) Money, income and causality. American Economic Review 62:540–552

    Google Scholar 

  • Sims CA (1980) Macroeconomics and reality. Econometrica 48:1–48

    Google Scholar 

  • Tiao GC, Box GEP (1981) Modeling multiple time series with application. Journal of the American Statistical Association 75:802–816

    Google Scholar 

  • Tiao GC, Box GEP, Grupe MR, Hudak GB, Bell WR, Chang I (1979) The Wisconsin multiple time series (WMTS-1) program. Department of Statistics, University of Wisconsin, Madison

    Google Scholar 

  • Tiao GC, Tsay RS (1983) Multiple time series modeling and extended sample cross-correlations. Journal of Business and Economic Statistics 1:43–56

    Google Scholar 

  • Vandaele W (1981) “TS computer programs” accessed through the University of of Oregon Computing Center

  • Wald A (1943) Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54:426–482

    Google Scholar 

  • Wallis K (1977) Multiple time series analysis and the final form of economic variables. Econometrica 45:1481–1497

    Google Scholar 

  • Wilson GT (1973) The estimation of parameters in multivariate time series models. Journal of Royal Statistics, Series B 35:76–85

    Google Scholar 

  • Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests of aggregation bias. Journal of the American Statistical Association 57:348–368

    Google Scholar 

  • Zellner A (1979) Causality and econometrics. Carnegie-Rochester Conference Series on Public Policy (supplement to Journal of Monetary Economics) 10:9–54

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management Science, California State University, Sacramento, 6000 J. Street, 95819-2694, Sacramento, CA, USA

    S. A. Taylor P.D.

Authors
  1. S. A. Taylor P.D.
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author would like to acknowledge numerous suggestions and insight provided by Bert Steece and Sergio Koreisha, along with two anonymous referees.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taylor, S.A. A comparison of classical tests of criterion when determining Granger causality with a bivariate ARMA model. Empirical Economics 14, 257–271 (1989). https://doi.org/10.1007/BF01972394

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01972394

Keywords

Search

Navigation