A Comparative Study on Additive and Mixed Models in Descriptive Time Series

Kelechukwu Celestine Nosike Dozie; Maxwell Azubuike Ijomah

doi:doi:10.11648/j.ajmcm.20200501.12

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A Comparative Study on Additive and Mixed Models in Descriptive Time Series

Kelechukwu Celestine Nosike Dozie, Maxwell Azubuike Ijomah

Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 1)

Received: 7 January 2020 Accepted: 27 January 2020 Published: 11 February 2020

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Abstract

Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.

Published in	American Journal of Mathematical and Computer Modelling (Volume 5, Issue 1)
DOI	10.11648/j.ajmcm.20200501.12
Page(s)	12-17
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), 2024. Published by Science Publishing Group

Keywords

Buys-Ballot Table, Time Series Decomposition, Additive Model, Mixed Model, Trend Parameter, Seasonal Indices

References

[1]	Dagum E. B. (2010). Time Series Modeling and Decomposition. Statistica, anno LXX, n. 4. 434-457.
[2]	Chatfield, C. (2004). The analysis of time Series: An introduction. Chapman and Hall,/CRC Press, Boca Raton.
[3]	Arz, S. (2006). A New Mixed Multiplicative-Additive Model for Seasonal Adjustment. Conference on seasonality, seasonal adjustment and their implications for short-term analysis and forecasting. Luxembourg, 10-12 May.
[4]	Iwueze S. I., Nwogu. E. C., Ohakwe, J., and Ajaraogu J. C. (2011). Uses of the Buys-Ballot Table in Time Series Analysis. Applied Mathematics, 2, 633-645.
[5]	Enegesele D. Iwueze I. S. & Ijomah M. A. (2017). Parametric and Non Parametric Approach to Choice of Model in Descriptive Time Series International Journal of Applied Science and Mathematical Theory, 3 (4), 15-22.
[6]	Iwueze, I. S. and Akpanta, A. C. (2009). “On Applying the Bartlett Transformation Method to Time Series Data”. Journal of Mathematical Sciences, Vol. 20, No. 3, pp. 227-243.
[7]	Linde, P. (2005). Seasonal Adjustment, Statistics Denmark. www.dst.dk/median/konrover/13-forecasting-org/seasonal/001pdf.
[8]	Gupta, S. C. (2013). Fundamentals of Statistics, Himalaya Publishing House PVT, LTD. Mumbai-400004.
[9]	Oladugba, A. V., Ukaegbu, E. C., Udom, A. U., Madukaife, M. S., Ugah, T. E. & Sanni, S. S., (2014). Principles of Applied Statistic, University of Nigeria Press Limited.
[10]	Iwueze, I. S. & Nwogu E. C. (2004). Buys-Ballot estimates for time series decomposition, Global Journal of Mathematics, 3 (2), 83-98.
[11]	C. H. D. Buys-Ballot, “Leo Claemert Periodiques de Temperature,” Kemint et Fills, Utrecht, 1847.
[12]	Iwueze S. I., Nwogu. E. C., and Ajaraogu J. C. (2015). Best Linear Unbiased Estimate using Buys-Ballot Procedure when Trend-Cycle Component is Linear. CBN Journal of Applied Statistics. 2 (1). 15–29.
[13]	Okororie C. 1, Egwim K. C., Eke C. N., and Onuoha D. O., (2013). Buys-Ballot Modeling of Nigerian Domestic Crude Oil Production. West African Journal of Industrial and Academic Research 8 (1), 160-171.
[14]	Iwueze, I. S. & Nwogu, E. C. (2014). Framework for choice of models and detection of seasonal effect in time series. Far East Journal of Theoretical Statistics 48 (1), 45-66.
[15]	Nwogu, E. C, Iwueze, I. S. Dozie, K. C. N. & Mbachu, H. I (2019). Choice between mixed and multiplicative models in time series decomposition. International Journal of Statistics and Applications. 9 (5), 153-159.

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APA Style

Kelechukwu Celestine Nosike Dozie, Maxwell Azubuike Ijomah. (2020). A Comparative Study on Additive and Mixed Models in Descriptive Time Series. American Journal of Mathematical and Computer Modelling, 5(1), 12-17. https://doi.org/10.11648/j.ajmcm.20200501.12

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ACS Style

Kelechukwu Celestine Nosike Dozie; Maxwell Azubuike Ijomah. A Comparative Study on Additive and Mixed Models in Descriptive Time Series. Am. J. Math. Comput. Model. 2020, 5(1), 12-17. doi: 10.11648/j.ajmcm.20200501.12

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AMA Style

Kelechukwu Celestine Nosike Dozie, Maxwell Azubuike Ijomah. A Comparative Study on Additive and Mixed Models in Descriptive Time Series. Am J Math Comput Model. 2020;5(1):12-17. doi: 10.11648/j.ajmcm.20200501.12

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@article{10.11648/j.ajmcm.20200501.12,
  author = {Kelechukwu Celestine Nosike Dozie and Maxwell Azubuike Ijomah},
  title = {A Comparative Study on Additive and Mixed Models in Descriptive Time Series},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {1},
  pages = {12-17},
  doi = {10.11648/j.ajmcm.20200501.12},
  url = {https://doi.org/10.11648/j.ajmcm.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200501.12},
  abstract = {Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.},
 year = {2020}
}

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TY  - JOUR
T1  - A Comparative Study on Additive and Mixed Models in Descriptive Time Series
AU  - Kelechukwu Celestine Nosike Dozie
AU  - Maxwell Azubuike Ijomah
Y1  - 2020/02/11
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200501.12
DO  - 10.11648/j.ajmcm.20200501.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 12
EP  - 17
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200501.12
AB  - Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.
VL  - 5
IS  - 1
ER  -

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Author Information

Kelechukwu Celestine Nosike Dozie

Department of Statistics Imo State University, Owerri, Imo State, Nigeria
Maxwell Azubuike Ijomah

Department of Mathematics/Statistics, University of Port Harcourt, Port Harcourt, Nigeria

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Plain Text BibTeX RIS

APA Style

Kelechukwu Celestine Nosike Dozie, Maxwell Azubuike Ijomah. (2020). A Comparative Study on Additive and Mixed Models in Descriptive Time Series. American Journal of Mathematical and Computer Modelling, 5(1), 12-17. https://doi.org/10.11648/j.ajmcm.20200501.12

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ACS Style

Kelechukwu Celestine Nosike Dozie; Maxwell Azubuike Ijomah. A Comparative Study on Additive and Mixed Models in Descriptive Time Series. Am. J. Math. Comput. Model. 2020, 5(1), 12-17. doi: 10.11648/j.ajmcm.20200501.12

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AMA Style

Kelechukwu Celestine Nosike Dozie, Maxwell Azubuike Ijomah. A Comparative Study on Additive and Mixed Models in Descriptive Time Series. Am J Math Comput Model. 2020;5(1):12-17. doi: 10.11648/j.ajmcm.20200501.12

Copy | Download

@article{10.11648/j.ajmcm.20200501.12,
  author = {Kelechukwu Celestine Nosike Dozie and Maxwell Azubuike Ijomah},
  title = {A Comparative Study on Additive and Mixed Models in Descriptive Time Series},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {1},
  pages = {12-17},
  doi = {10.11648/j.ajmcm.20200501.12},
  url = {https://doi.org/10.11648/j.ajmcm.20200501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200501.12},
  abstract = {Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Comparative Study on Additive and Mixed Models in Descriptive Time Series
AU  - Kelechukwu Celestine Nosike Dozie
AU  - Maxwell Azubuike Ijomah
Y1  - 2020/02/11
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200501.12
DO  - 10.11648/j.ajmcm.20200501.12
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 12
EP  - 17
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200501.12
AB  - Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.
VL  - 5
IS  - 1
ER  -

Copy | Download