American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2014, 2(1), 47-52
DOI: 10.12691/ajams-2-1-8
Open AccessArticle

Penalties for Misclassification of a Pure Diagonal Bilinear Process of Order Two as a Moving Average Process of Order Two

O. E. Okereke1, , I. S. Iwueze2 and C. O. Omekara1

1Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

2Department of Statistics, Federal University of Technology, Owerri, Imo State, Nigeria

Pub. Date: February 11, 2014

Cite this paper:
O. E. Okereke, I. S. Iwueze and C. O. Omekara. Penalties for Misclassification of a Pure Diagonal Bilinear Process of Order Two as a Moving Average Process of Order Two. American Journal of Applied Mathematics and Statistics. 2014; 2(1):47-52. doi: 10.12691/ajams-2-1-8

Abstract

The penalty function based on misclassification of a pure diagonal bilinear process of order two as a moving process of order two was derived in this study. Computation of penalties using the penalty function revealed that such misclassification increases the error variance. Regression analysis of the penalties on the parameters of the pure diagonal bilinear process suggested a second order polynomial regression model. A test of significance of each of the parameters of the fitted model showed that all the parameter estimates were statistically significant at 5% level of significance. The analysis of variance technique was also used to confirm the adequacy of the fitted model.

Keywords:
autocorrelation function penalty function pure diagonal bilinear process moving average process polynomial regression

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References:

[1]  Bessels, S. (2006). One step beyond the solvable equation. www.staff.science.uu.nc/…/Afstudeerscriptie_Sander_Bessels.pdf (This site was visited in June, 2013).
 
[2]  Box, G. E. P., Jenkins, G. M. and Reinsel, G. C.(1994). Time Series Analysis: Forecasting and Control. 3rd ed., Prentice-Hall, Englewood Cliffs, N. J.
 
[3]  Chatfield, C. (1995). The Analysis of Time Series. An Introduction. 5th ed. Chapmann and Hall, London.
 
[4]  Granger, C. W. J. and Andersen, A. (1978). An Introduction to Bilinear Time Series Models. Vanderhoeck and Ruprecht, Gottingen.
 
[5]  Hahn, K. (2005). Solving cubic and quartic polynomials. www.Karlscalculus.org/pdf/cubicquartic.pdf.
 
[6]  Iwueze, I. S. and Ohakwe, J. (2009). Penalties for misclassification of first order and linear moving average time series processes. Interstat Journal of Statistics, No3, http//interstatjournals.net/Year/2009/articles/0906003.pdf.
 
[7]  Okereke, O. E. (2013). Characterization of moments of pure diagonal bilinear process of order two and moving average process of order two, Unpublished Ph. D Dissertation.
 
[8]  Okereke, O. E and Iwueze, I. S. (2013). Region of comparison for the second order moving average and pure diagonal bilinear processes. International Journal of Applied Mathematics and Statistical Sciences, 2(2): 17-25.
 
[9]  Okereke, O. E, Iwueze, I. S and Johnson, O. (2013). Extrema for autocorrelation coefficients of moving average processes. Far East Journal of Theoritical Statistics, 42(2): 137-150.
 
[10]  Wei, W. W. S. (2006). Time Series Analysis, Univariate and Multivariate Methods. 2nd ed. Pearson Addision Wesley, New York.