Abstract
AR and bilinear time series models are expressed as time series chain graphical models, based on which, it is shown that the coefficients of AR and bilinear models are the conditional correlation coefficients conditioned on the other components of the time series. Then a graphically based procedure is proposed to test the significance of the coefficients of AR and bilinear time series. Simulations show that our procedure performs well both in sizes and powers.
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References
Brillinger D R. Remarks concerning graphical models for time series and point processes. Rev Econometrica, 16: 1–23 (1996)
Cox D R, Wermuth N. Multivariate Dependencies—Models, Analysis and Interpretation. London: Chapman & Hall, 1996
Edwards D. Introduction to Graphical Modelling. New York: Springer-Verlag, 2000
Lauritzen S L. Graphical Models. Oxford: Oxford University Press, 1996
Whittaker J. Graphical Models in Applied Multivariate Statistics. Chichester: John Wiley, 1990
Dahlhaus R, Eichler M. Causality and graphical models for time series. In: Green P, Hjort N, Richardson S, eds. Highly Structured Stochastic Systems. Oxford: University Press, 2002
Eichler M. Graphical modelling of time series. Preprint, University Heidelberg, 2001
Eichler M. Granger-causality and path diagrams for multivariate time series. J Econometrics, 137(2): 334–353 (2007)
Oxley L, Reale M, Wilson G T. Finding directed acyclic graphs for vector autoregressions. In: Antoch J, ed. Proceedings in Computational Statistics. Heidelberg: Physical-Verlag, 2004, 1621–1628
Real M, Wilson G T. The sampling properties of conditional independence graphs for structural vector autoregression. Biometrika, 8: 7–461 (2002)
Thiesson B, Chickering D M, Heckerman D, et al. ARMA time-series modelling with graphical models. In: Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence, Banff, Canada. Coruallis, OR: AUAI Press, 2004, 552–560
Brockwell P J, Davis R A. Time Series: Theory and Methods. New York: Springer-Verlag, 1988
Shao J. Mathematical Statistics. New York: Springer-Verlag, 1999
Liu J. On stationarity and asymptotic inference of bilinear time series models. Statist Sin, 2: 479–494 (1992)
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This work was supported by the Hong Kong Polytechnic University Research Council, the National Natural Science Foundation of China (Grant No. 10671044) and the Science and Technology Bureau of Guangzhou Municipal Government of China (Grant No. LSBH-017)
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Ip, W., Wong, H., Li, Y. et al. Testing coefficients of AR and bilinear time series models by a graphical approach. Sci. China Ser. A-Math. 51, 2304–2314 (2008). https://doi.org/10.1007/s11425-008-0082-3
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DOI: https://doi.org/10.1007/s11425-008-0082-3