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A test for the equivalence ofk ARMA models

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Conclusion

This paper has suggested a method for determining the equivalence of multiple time series when the series are not necessarily independent. By borrowing on the seemingly-unrelated time series structure and employing separate induced tests the researcher is presented with a technique for inferring equivalence between series, and in its absence identifying the structural elements causing non-equivalence. The proposed approach is thought to be simpler to apply than previous methods, less demanding of computational resources and overcomes at least two major difficulties (the assumption of independence and the problem of extending the results to more than two series, inherent in earlier time series equivalence determination strategies.

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References

  • Christensen, L.: Simultaneous Statistical Inference in the Normal Linear Regression Model. Journal of the American Statistical Society68, 1973, 457–461.

    Google Scholar 

  • Fearon, H.: The Arizona Economy: A Review and Recap of the Purchasing Agent's Monthly Survey. Arizona Business, 1968.

  • Gallant, A., andA. Holly: Statistical Inference in an Implicit, Nonlinear Simultaneous Equation Model in the Context of Maximum Likelihood. Econometrics48, 1980, 697–720.

    Google Scholar 

  • Goodman, L.A., andY. Grundfeld: Some Nonparametric Tests for Comovements Between Time Series. Journal of the American Statistical Association56, 1961, 11–26.

    Google Scholar 

  • Haugh, L.D.: Checking the Independence of Two Covariance-Stationary Time Series: A Univariate Residual Cross-Correlation Approach. Journal of the American Statistical Association, Vol. 71. 1976, 378–385.

    Google Scholar 

  • Hillmer, S., andG. Tiao: Likelihood Function of Stationary Multiple Autoregressive Moving Average Models. Journal of the American Statistical Society74, 1979, 652–660.

    Google Scholar 

  • Hsu, D.A., andJ.S. Hunter: Analysis of Simulation-Generated Responses Using Autoregressive Models. Management Science24, 1977, 181–190.

    Google Scholar 

  • Lehmann, E.: A Theory of Some Multiple Decision Problems I. Annals of Mathematical Statistics28, 1957a, 1–25.

    Google Scholar 

  • —: A Theory of Some Multiple Decision Problems II. Annals of Mathematical Statistics28, 1957b. 547–572.

    Google Scholar 

  • Ljung, G.M., andG.E.P. Box: On a Measure of Lack of Fit in Timer Series Models. Biometrika65, 1978, 297–303.

    Google Scholar 

  • Miller, R.: Simultaneous Statistical Inference. New York: McGraw-Hill, 1966

    Google Scholar 

  • Moore, G.H., andW.A. Wallis: Time Series Significance Tests Based on Signs of Differences. Journal of the American Statistical Association38, 1943, 153–164.

    Google Scholar 

  • Moriarty, M., andG. Salomon: Estimation and Forecast Performance of a Multivariate Time Series Model of Sales. Journal of Marketing Research17, 1980, 558–564.

    Google Scholar 

  • Nelson, C.: Gains in Efficiency from Joint Estimation of Systems of ARMA Processes. Journal of Econometrics4, 1976, 331–348.

    Article  Google Scholar 

  • Parsons, L., andW.A. Henry: Testing Equivalence of Observed and Generated Time Series by Spectral Methods. Journal of Marketing Research IX, 1973, 391–395.

    Google Scholar 

  • Pierce, D.A.: Relationships — and the Lack Thereof — Between Economic Time Series with Special Reference to Money and Interest Rates. Journal of the American Statistical Association72, 1977, 11–22.

    Google Scholar 

  • Roy, S.: On a Heuristic Method of Test Construction and Its Uses in Multivariate Analysis. Annals of Mathematical Statistics24, 1953, 220–239.

    Google Scholar 

  • Scheffe, H.: The Analysis of Variance. New York: John Wiley and Sons, 1959.

    Google Scholar 

  • Seber, G.: Linear Hypotheses and Induced Tests. Biometrika51, 1964, 41–47.

    Google Scholar 

  • Sen P.K.: Some Non-Parametric Tests for m-Dependent Time Series. Journal of the American Statistical Association, 1965, 134–147.

  • Tiao, G., andG. Box: Modeling Multiple Time Series with Applications. Journal of the American Statistical Association76, 1981, 802–816.

    Google Scholar 

  • Umashankar, S., andJ. Ledolter. Forecasting with Diagonal Multiple Time Series Models: An Extension of Univariate Models. Journal of Marketing Research20, 1983, 58–63.

    Google Scholar 

  • Whittle, P.: Gaussian Estimation in Stationary Time Series. Bulletin of the International Statistical Institute33, 1961, 105–129.

    Google Scholar 

  • Wood, S.: Forecasting Hospital Patient Census: Commonalities in Time Series. Health Service Research4, 1976, 107–119.

    Google Scholar 

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Steece, B., Wood, S. A test for the equivalence ofk ARMA models. Empirical Economics 10, 1–11 (1985). https://doi.org/10.1007/BF01988278

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  • DOI: https://doi.org/10.1007/BF01988278

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