On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model

Dike A. O.; Otuonye E. L.; Chikezie D. C.; Sambo D.

doi:doi:10.11648/j.ajtas.20160505.15

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On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model

Dike A. O., Otuonye E. L., Chikezie D. C., Sambo D.

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 19 May 2016 Accepted: 1 July 2016 Published: 17 August 2016

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Abstract

This paper examines the inverse cube transformation of error component of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the was mathematically proved as a proper pdf since The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.15
Page(s)	280-284
Creative Commons	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), 2016. Published by Science Publishing Group

Keywords

Power Transformations, Probability Density Function Error Component, Mean Variance, Multiplicative Time Series

References

[1]	Ajibade B. F, Nwosu C. R and Mbegdu J. I. (2015). The Distribution of the Inverse Square Root Transformed Error Component of The Multiplicative Time Series Model. Journal of Modern Applied Statistical Methods. Vol. 14. Issue 2. pp 171-199.
[2]	Akpanta A. C. and Iwueze I. S (2009). On Applying the Bartlett Transformation Methods to Time Series Data. Journal of Mathematical Sciences Vol. 20, No. 3. Pp 227-243.
[3]	Bartlett, M. S. (1947). The use of transformations, Biometrics, 3, 39-52.
[4]	Box, G. E. P. and Cox, D. R. (1964). An Analysis of Transformations. J. Roy. Statist. Soc., B-26, 2 11-243, discussion 244-252.
[5]	Chartfield C. (1980). The Analysis of Time Series; An Introduction, Chapman & Hall, London.
[6]	Ibeh G. C and Nwosu C. R. (2013). Study on the Error Component of Multiplicative Time Series Model under Inverse Square Transformation. American Journal of Mathematics and Statistics (396): pp 362-374.
[7]	Iwueze Iheanyi S. (2007). Some Implications of Truncating the N (1, a 2) Distribution to the left at Zero. Journal of Applied Sciences. 7 (2) (2007) pp 189-195.
[8]	Iwueze I. S, Nwogu E. C., Ohakwe J and Ajaraogu J. C, (201 1). New Uses of Buys-Ballot Table. Journal of Applied Mathematics, 2011, 2. 633-645. DOT: 10.4236/am.2011.25084.
[9]	Iwueze, I. S., Nwogu, E. C. and Ajaraogu, J. C. (2011). Uses of the Buys-Ballot Table in Time Series Analysis. Journal of Applied Mathematics, 2, 633-645.
[10]	Iwueze, I. S. and Nwogu, E. C. (2004). Buys-Ballot for Time Series Decomposition. Global Journal of Mathematical Science, 3 (2): 83-89.
[11]	Nwosu C. R, Iwueze I. S. and Ohakwe J. (2010). Distribution of the Error Term of the Multiplicative Time Series Model Under Inverse Transformation. Journal of Advances and Applications in Mathematical Sciences. Volume 7, Issue 2, 2010, pp. 119-139
[12]	Ohakwe J, Iwuoha O. and Otuonye E. L (2013). Condition for Successful Square Transformation in Time Series Modeling. Journal of Applied MathematicsVol. 4. pp 680-687.
[13]	Okereke O. E. and Omekare C. O. (2010) On the Properties of the Truncated Normal Distribution and its Square Root Transformation. Journal of the Nigerian Statistical Association. Vol. 22, 2010, pp 37-43.
[14]	Osborne, J. (2002). Notes on the Use of Data Transformations, J. Practice Practical Assessment, Research &Evaluation, 8 (6).
[15]	Otuony E. L, Iwueze I. S. and Ohakwe J. (2011). The Effect of Square Root Transformation on the Error Component of the Multiplicative Time Series Model. International Journal of Statistics and Systems. Vol. 6, No. 4, 2011, pp. 461 - 476. ISSN: 0973-2675
[16]	Ohakwe, J., Dike, O. A. and Akpanta, A. C (2012). The Implication of Square Root Transformation on a Gamma Distribution Error Component of a Multiplicative Time Series Model, Proceedings of African Regional Conference on Sustainable Development, Vol. 6, No. 4, 2012, pp. 65-78.
[17]	Wei, W. W. (1990). Time Series Analysis: Multivariate Methods. Addision-Wesley Publishing Company, Inc., Redwood City.

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Dike A. O., Otuonye E. L., Chikezie D. C., Sambo D. (2016). On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. American Journal of Theoretical and Applied Statistics, 5(5), 280-284. https://doi.org/10.11648/j.ajtas.20160505.15

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ACS Style

Dike A. O.; Otuonye E. L.; Chikezie D. C.; Sambo D. On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. Am. J. Theor. Appl. Stat. 2016, 5(5), 280-284. doi: 10.11648/j.ajtas.20160505.15

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AMA Style

Dike A. O., Otuonye E. L., Chikezie D. C., Sambo D. On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. Am J Theor Appl Stat. 2016;5(5):280-284. doi: 10.11648/j.ajtas.20160505.15

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@article{10.11648/j.ajtas.20160505.15,
  author = {Dike A. O. and Otuonye E. L. and Chikezie D. C. and Sambo D.},
  title = {On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {280-284},
  doi = {10.11648/j.ajtas.20160505.15},
  url = {https://doi.org/10.11648/j.ajtas.20160505.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.15},
  abstract = {This paper examines the inverse cube transformation of error component  of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the  was mathematically proved as a proper pdf since  The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.},
 year = {2016}
}

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TY  - JOUR
T1  - On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model
AU  - Dike A. O.
AU  - Otuonye E. L.
AU  - Chikezie D. C.
AU  - Sambo D.
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DO  - 10.11648/j.ajtas.20160505.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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PB  - Science Publishing Group
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AB  - This paper examines the inverse cube transformation of error component  of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the  was mathematically proved as a proper pdf since  The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.
VL  - 5
IS  - 5
ER  -

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Author Information

Dike A. O.

Department of Maths and Statistics, AkanuIbiam Federal Polytechnic, Unwana, Afikpo, Nigeria
Otuonye E. L.

Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, Uturu, Nigeria
Chikezie D. C.

Department of Statistics, Faculty of Biological and Physical Sciences, Abia State University, Uturu, Nigeria
Sambo D.

Department of Maths and Statistics, AkanuIbiam Federal Polytechnic, Unwana, Afikpo, Nigeria

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APA Style

Dike A. O., Otuonye E. L., Chikezie D. C., Sambo D. (2016). On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. American Journal of Theoretical and Applied Statistics, 5(5), 280-284. https://doi.org/10.11648/j.ajtas.20160505.15

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ACS Style

Dike A. O.; Otuonye E. L.; Chikezie D. C.; Sambo D. On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. Am. J. Theor. Appl. Stat. 2016, 5(5), 280-284. doi: 10.11648/j.ajtas.20160505.15

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AMA Style

Dike A. O., Otuonye E. L., Chikezie D. C., Sambo D. On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model. Am J Theor Appl Stat. 2016;5(5):280-284. doi: 10.11648/j.ajtas.20160505.15

Copy | Download

@article{10.11648/j.ajtas.20160505.15,
  author = {Dike A. O. and Otuonye E. L. and Chikezie D. C. and Sambo D.},
  title = {On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {280-284},
  doi = {10.11648/j.ajtas.20160505.15},
  url = {https://doi.org/10.11648/j.ajtas.20160505.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.15},
  abstract = {This paper examines the inverse cube transformation of error component  of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the  was mathematically proved as a proper pdf since  The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On Properties of the Inverse Cube Transformation of Error Component of the Multiplicative Time Series Model
AU  - Dike A. O.
AU  - Otuonye E. L.
AU  - Chikezie D. C.
AU  - Sambo D.
Y1  - 2016/08/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.15
DO  - 10.11648/j.ajtas.20160505.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 280
EP  - 284
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.15
AB  - This paper examines the inverse cube transformation of error component  of multiplicative time series model. The probability density function (pdf) of the inverse cube root transformation of the multiplicative time series model was established, Further the  was mathematically proved as a proper pdf since  The Statistical properties (mean and variance) of the inverse cube transformation were equally shown.
VL  - 5
IS  - 5
ER  -

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