American Journal of Theoretical and Applied Statistics

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Necessary Conditions for Isolation of Special Classes of Bilinear Autoregressive Moving Average Vector (BARMAV) Models

Received: Jul. 22, 2018    Accepted: Aug. 07, 2018    Published: Sep. 04, 2018
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Abstract

Bilinear Autoregressive Moving Average Vector (BARMAV) Models are models aggregated with the linear and non-linear vector components of autoregressive and moving average processes. The linear part is the sum of the two vector processes, while the non-linear part is the product of the processes. From the general BARMAV models, Bilinear Autoregressive Vector (BARV) Models and Bilinear Moving Average Vector (BMAV) Models have been isolated. Under certain conditions, the models are proved to exist. Empirically, Nigerian consumer price index and inflation rate are used to test the fitness of the bilinear models. Data for the analysis are from Central Bank of Nigeria Statistical Bulletin, collected from January 2009 to December 2016 with November 2009 as the base year for each of the series. The bilinear autoregressive moving average vector models are fitted to the data. Parameters are tested and found to be significant. The adequacy of each estimated model is confirmed with ACF, PACF and descriptive statistics adopted in the paper. The plots of the actual and fitted CPI and IR have shown that models are adequate as estimates compete favourably with the actual values. The models are useful in modelling some economic and financial data that exhibit some characteristics of non-linearity.

DOI 10.11648/j.ajtas.20180705.13
Published in American Journal of Theoretical and Applied Statistics ( Volume 7, Issue 5, September 2018 )
Page(s) 180-187
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

AR Process, MA Process, Linear and Bilinear Models

References
[1] Bibi, A. and Oyet, A. J. (1991): Estimation of some bilinear time series models with time varying coefficients, AMS.
[2] Box, G. P. and Jenkins, G. M (1978): Time Series Analysis, Forecasting and Control. Holden-Day, San Francisco.
[3] Dufour Jean-Marie (2006): Multivariate Time Series Modelling. Cambridge University Press, Cambridge, U.K.
[4] Granger, C. W. J. and Anderson, A. P (1978): Introduction to Bilinear Time Series Models. Vandenhoeck and Ruprecht.
[5] Gujarati, Damodar N.and Porter, Dawn C. (2009): Basic Econometrics, Fifth Edition.
[6] Harrison L., Penny, W. D. and Friston, K. J. (2003): Application of multivariate time series in the functional network in the brain region. Neuroimage, 19(4), 1477-1491.
[7] Iwueze S. I. (2002): Vectorial representation and its application to covariance analysis of super-diagonal bilinear time series models. The Physical Scientist 1(1), 85-96.
[8] Johnston Jack and DiNardo John (1997): Econometric Methods. International Edition.
[9] Kendell M. and Ord Keith J. (1990): Time Series. Third Edition, Halsted Press, Third Avenue, New York.
[10] Maravall, A. (1983): An application of non-linear time series forecasting. Journal of Business and Economic Statistics Vol. 1 (1), 66-74.
[11] Sims, C. A. (1996): Multivariate Time Series Modelling of Gross National Products of United State of America. American Statistical Association Meetings.
[12] Subba Rao, T. and Gabr, M. M. (1984): An introduction to bispectral analysis and bilinear time series models. Lecture Notes in Statistics No.24. Springer Verlag.
[13] Usoro, A. E. and Omekara, C. O. (2007): Estimation of Pure Autoregressive Models for Revenue Series. Global Journal of Mathematical Sciences, 6(1), 31-37.
[14] Usoro, A. E. and Omekara C. O. (2008): Bilinear autoregressive vector models and their applications to estimation of revenue series. Asian Journal of Mathematics and Statistics 1(1): 50-56.
[15] Usoro, Anthony E. (2017): Identification of Classes of Bilinear Time Series Models. Journal of Statistics; Advances in Theory and Applications. Vol.17, No.2. 153-160.
[16] Usoro, Anthony E. (2018): Modelling of Nigerian gross domestic product using seasonal and bilinear autoregressive integrated moving average models. Journal of Statistical and Econometric Methods, Vol.7, Issue 2.
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  • APA Style

    Anthony Effiong Usoro, Eyo Awakessien Clement. (2018). Necessary Conditions for Isolation of Special Classes of Bilinear Autoregressive Moving Average Vector (BARMAV) Models. American Journal of Theoretical and Applied Statistics, 7(5), 180-187. https://doi.org/10.11648/j.ajtas.20180705.13

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    ACS Style

    Anthony Effiong Usoro; Eyo Awakessien Clement. Necessary Conditions for Isolation of Special Classes of Bilinear Autoregressive Moving Average Vector (BARMAV) Models. Am. J. Theor. Appl. Stat. 2018, 7(5), 180-187. doi: 10.11648/j.ajtas.20180705.13

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    AMA Style

    Anthony Effiong Usoro, Eyo Awakessien Clement. Necessary Conditions for Isolation of Special Classes of Bilinear Autoregressive Moving Average Vector (BARMAV) Models. Am J Theor Appl Stat. 2018;7(5):180-187. doi: 10.11648/j.ajtas.20180705.13

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  • @article{10.11648/j.ajtas.20180705.13,
      author = {Anthony Effiong Usoro and Eyo Awakessien Clement},
      title = {Necessary Conditions for Isolation of Special Classes of Bilinear Autoregressive Moving Average Vector (BARMAV) Models},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {7},
      number = {5},
      pages = {180-187},
      doi = {10.11648/j.ajtas.20180705.13},
      url = {https://doi.org/10.11648/j.ajtas.20180705.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20180705.13},
      abstract = {Bilinear Autoregressive Moving Average Vector (BARMAV) Models are models aggregated with the linear and non-linear vector components of autoregressive and moving average processes. The linear part is the sum of the two vector processes, while the non-linear part is the product of the processes. From the general BARMAV models, Bilinear Autoregressive Vector (BARV) Models and Bilinear Moving Average Vector (BMAV) Models have been isolated. Under certain conditions, the models are proved to exist. Empirically, Nigerian consumer price index and inflation rate are used to test the fitness of the bilinear models. Data for the analysis are from Central Bank of Nigeria Statistical Bulletin, collected from January 2009 to December 2016 with November 2009 as the base year for each of the series. The bilinear autoregressive moving average vector models are fitted to the data. Parameters are tested and found to be significant. The adequacy of each estimated model is confirmed with ACF, PACF and descriptive statistics adopted in the paper. The plots of the actual and fitted CPI and IR have shown that models are adequate as estimates compete favourably with the actual values. The models are useful in modelling some economic and financial data that exhibit some characteristics of non-linearity.},
     year = {2018}
    }
    

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    AB  - Bilinear Autoregressive Moving Average Vector (BARMAV) Models are models aggregated with the linear and non-linear vector components of autoregressive and moving average processes. The linear part is the sum of the two vector processes, while the non-linear part is the product of the processes. From the general BARMAV models, Bilinear Autoregressive Vector (BARV) Models and Bilinear Moving Average Vector (BMAV) Models have been isolated. Under certain conditions, the models are proved to exist. Empirically, Nigerian consumer price index and inflation rate are used to test the fitness of the bilinear models. Data for the analysis are from Central Bank of Nigeria Statistical Bulletin, collected from January 2009 to December 2016 with November 2009 as the base year for each of the series. The bilinear autoregressive moving average vector models are fitted to the data. Parameters are tested and found to be significant. The adequacy of each estimated model is confirmed with ACF, PACF and descriptive statistics adopted in the paper. The plots of the actual and fitted CPI and IR have shown that models are adequate as estimates compete favourably with the actual values. The models are useful in modelling some economic and financial data that exhibit some characteristics of non-linearity.
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Author Information
  • Department of Mathematics and Statistics, Akwa Ibom State University, Mkpat Enin, Nigeria

  • Department of Mathematics and Statistics, Akwa Ibom State University, Mkpat Enin, Nigeria

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