Uses of the Buys-Ballot Table in Time Series Analysis

ABSTRACT

Uses of the Buys-Ballot table for choice of appropriate transformation (using the Bartlett technique), assessment of trend and seasonal components and choice of model for time series decomposition are discussed in this paper. Uses discussed are illustrated with numerical examples when trend curve is linear, quadratic and exponential.

Uses of the Buys-Ballot table for choice of appropriate transformation (using the Bartlett technique), assessment of trend and seasonal components and choice of model for time series decomposition are discussed in this paper. Uses discussed are illustrated with numerical examples when trend curve is linear, quadratic and exponential.

KEYWORDS

Buys-Ballot Table, Trend Assessment, Assessment of Seasonality, Periodic Averages, Seasonal Averages, Data Transformation, Choice of Model

Buys-Ballot Table, Trend Assessment, Assessment of Seasonality, Periodic Averages, Seasonal Averages, Data Transformation, Choice of Model

Cite this paper

nullI. Iwueze, E. Nwogu, O. Johnson and J. Ajaraogu, "Uses of the Buys-Ballot Table in Time Series Analysis,"*Applied Mathematics*, Vol. 2 No. 5, 2011, pp. 633-645. doi: 10.4236/am.2011.25084.

nullI. Iwueze, E. Nwogu, O. Johnson and J. Ajaraogu, "Uses of the Buys-Ballot Table in Time Series Analysis,"

References

[1] C. Chatfield, “The Analysis of Time Series: An Introduction,” Chapman and Hall/CRC Press, Boca Raton, 2004.

[2] D. B. Percival and A. T. Walden, “Wavelet Methods for Time Series Analysis,” Cambridge University Press, Cambridge, 2000.

[3] M. B. Priestley, “Spectral Analysis and Time Series Analysis,” Academic Press, London, Vol. 1-2, 1981.

[4] G. E. P. Box, G. M. Jenkins and G. C. Reinsel, “Time Series Analysis, Forecasting and Control,” 3rd Edition, Prentice-Hall, Englewood Cliffs, 1994.

[5] W. W. S. Wei, “Time Series Analysis: Univariate and Multivariate Methods,” Addison-Wesley, Redwood City, 1989.

[6] M. G. Kendal and J. K. Ord, “Time Series,” 3rd Edition, Charles Griffin, London, 1990.

[7] G. M. Ljung and G. E. P. Box, “On a Measure of Lack of Fit in Time Series Models,” Biometrika, Vol. 65, No. 2, 1978, pp. 297-303. doi:10.1093/biomet/65.2.297

[8] H. Wold, “A Study in the Analysis of Stationary Time Series,” 2nd Edition, Almqrist and Witsett, Stockholm, 1938.

[9] C. H. D. Buys-Ballot, “Leo Claemert Periodiques de Temperature,” Kemint et Fills, Utrecht, 1847.

[10] I. S. Iwueze and A. C. Akpanta, “Effect of the Logarithmic Transformation on the Trend-Cycle Component,” Journal of Applied Science, Vol. 7, No. 17, 2007, pp. 2414-2422.

[11] I. S. Iwueze and E. C. Nwogu, “Buys-Ballot Estimates for Time Series Decomposition,” Global Journal of Mathematics, Vol. 3, No. 2, 2004, pp. 83-98.

[12] I. S. Iwueze and J. Ohakwe, “Buys-Ballot Estimates When Stochastic Trend is Quadratic,” Journal of the Nigerian Association of Mathematical Physics, Vol. 8, 2004, pp. 311-318.

[13] I. S. Iwueze and E. C. Nwogu “Buys-Ballot Estimates for Exponential and S-Shaped Curves, for Time Series,” Journal of the Nigerian Association of Mathematical Physics, Vol. 9, 2005, pp 357-366.

[14] I. S. Iwueze, E. C. Nwogu and J. C. Ajaraogu, “Properties of the Buys-Ballot Estimates When Trend-Cycle Component of a Time Series is Linear: Additive Case,” International Journal of Methematics and Computation, Vol. 8, No. S10, 2010, pp. 18-27.

[15] G. E. P. Box and D. R. Cox, “An Analysis of Transformations,” Journal of the Royal Statistical Society, Series B, Vol. 26, No. 2, 1964, pp. 211-243.

[16] A. C. Akpanta and I. S. Iwueze, “On Applying the Bartlett Transformation Method to Time Series Data,” Journal of Mathematical Sciences, Vol. 20, No. 3, 2009, pp. 227-243.

[17] M. S. Bartlett, “The Use of Transformations,” Biometrika, Vol. 3, 1947, pp. 39-52.

[18] R. V. Hogg and A. T. Craig, “Introduction to Mathematical Statistics,” 4th Edition, MacMillan Publishing Company, New York, 1978.

[19] Central Bank of Nigeria, The Statistical Bulletin, Vol. 18, 2007.

[1] C. Chatfield, “The Analysis of Time Series: An Introduction,” Chapman and Hall/CRC Press, Boca Raton, 2004.

[2] D. B. Percival and A. T. Walden, “Wavelet Methods for Time Series Analysis,” Cambridge University Press, Cambridge, 2000.

[3] M. B. Priestley, “Spectral Analysis and Time Series Analysis,” Academic Press, London, Vol. 1-2, 1981.

[4] G. E. P. Box, G. M. Jenkins and G. C. Reinsel, “Time Series Analysis, Forecasting and Control,” 3rd Edition, Prentice-Hall, Englewood Cliffs, 1994.

[5] W. W. S. Wei, “Time Series Analysis: Univariate and Multivariate Methods,” Addison-Wesley, Redwood City, 1989.

[6] M. G. Kendal and J. K. Ord, “Time Series,” 3rd Edition, Charles Griffin, London, 1990.

[7] G. M. Ljung and G. E. P. Box, “On a Measure of Lack of Fit in Time Series Models,” Biometrika, Vol. 65, No. 2, 1978, pp. 297-303. doi:10.1093/biomet/65.2.297

[8] H. Wold, “A Study in the Analysis of Stationary Time Series,” 2nd Edition, Almqrist and Witsett, Stockholm, 1938.

[9] C. H. D. Buys-Ballot, “Leo Claemert Periodiques de Temperature,” Kemint et Fills, Utrecht, 1847.

[10] I. S. Iwueze and A. C. Akpanta, “Effect of the Logarithmic Transformation on the Trend-Cycle Component,” Journal of Applied Science, Vol. 7, No. 17, 2007, pp. 2414-2422.

[11] I. S. Iwueze and E. C. Nwogu, “Buys-Ballot Estimates for Time Series Decomposition,” Global Journal of Mathematics, Vol. 3, No. 2, 2004, pp. 83-98.

[12] I. S. Iwueze and J. Ohakwe, “Buys-Ballot Estimates When Stochastic Trend is Quadratic,” Journal of the Nigerian Association of Mathematical Physics, Vol. 8, 2004, pp. 311-318.

[13] I. S. Iwueze and E. C. Nwogu “Buys-Ballot Estimates for Exponential and S-Shaped Curves, for Time Series,” Journal of the Nigerian Association of Mathematical Physics, Vol. 9, 2005, pp 357-366.

[14] I. S. Iwueze, E. C. Nwogu and J. C. Ajaraogu, “Properties of the Buys-Ballot Estimates When Trend-Cycle Component of a Time Series is Linear: Additive Case,” International Journal of Methematics and Computation, Vol. 8, No. S10, 2010, pp. 18-27.

[15] G. E. P. Box and D. R. Cox, “An Analysis of Transformations,” Journal of the Royal Statistical Society, Series B, Vol. 26, No. 2, 1964, pp. 211-243.

[16] A. C. Akpanta and I. S. Iwueze, “On Applying the Bartlett Transformation Method to Time Series Data,” Journal of Mathematical Sciences, Vol. 20, No. 3, 2009, pp. 227-243.

[17] M. S. Bartlett, “The Use of Transformations,” Biometrika, Vol. 3, 1947, pp. 39-52.

[18] R. V. Hogg and A. T. Craig, “Introduction to Mathematical Statistics,” 4th Edition, MacMillan Publishing Company, New York, 1978.

[19] Central Bank of Nigeria, The Statistical Bulletin, Vol. 18, 2007.