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Functional coefficient autoregressive conditional root model

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Abstract

This paper proposes an extended model based on ACR model: Functional coefficient autoregressive conditional root model (FCACR). Under some assumptions, the authors show that the process is geometrically ergodic, stationary and all moments of the process exist. The authors use the polynomial spline function to approximate the functional coefficient, and show that the estimate is consistent with the rate of convergence O p (h ν+1 + n −1/3). By simulation study, the authors discover the proposed method can approximate well the real model. Furthermore, the authors apply the model to real exchange rate data analysis.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

    Jianjun Zhou

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Min Chen

Authors
  1. Jianjun Zhou
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  2. Min Chen
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Corresponding author

Correspondence to Jianjun Zhou.

Additional information

This research was supported by the National Nature Science Foundation of China under Grant Nos. 10961026, 11171293, 71003100, 70221001, 70331001, and 10628104, the Ph.D. Special Scientific Research Foundation of Chinese University under Grant No. 20115301110004, Key Fund of Yunnan Province under Grant No. 2010CC003, the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China under Grant No. 11XNK027.

This paper was recommended for publication by Editor Guohua ZOU.

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Zhou, J., Chen, M. Functional coefficient autoregressive conditional root model. J Syst Sci Complex 25, 998–1013 (2012). https://doi.org/10.1007/s11424-012-0198-y

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  • DOI: https://doi.org/10.1007/s11424-012-0198-y

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