Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations

Samuel Olorunfemi Adams; Yahaya Haruna Umar

doi:doi:10.11648/j.ajtas.20200905.15

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Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations

Samuel Olorunfemi Adams, Yahaya Haruna Umar

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)

Received: 15 June 2020 Accepted: 7 July 2020 Published: 12 October 2020

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Abstract

Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)
DOI	10.11648/j.ajtas.20200905.15
Page(s)	219-227
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), 2020. Published by Science Publishing Group

Keywords

Time Series Predicting, Generalized Cross Validation, Mallow’s CP Criterion, Hybrid GCV-MCP

References

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APA Style

Samuel Olorunfemi Adams, Yahaya Haruna Umar. (2020). Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. American Journal of Theoretical and Applied Statistics, 9(5), 219-227. https://doi.org/10.11648/j.ajtas.20200905.15

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ACS Style

Samuel Olorunfemi Adams; Yahaya Haruna Umar. Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. Am. J. Theor. Appl. Stat. 2020, 9(5), 219-227. doi: 10.11648/j.ajtas.20200905.15

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AMA Style

Samuel Olorunfemi Adams, Yahaya Haruna Umar. Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. Am J Theor Appl Stat. 2020;9(5):219-227. doi: 10.11648/j.ajtas.20200905.15

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@article{10.11648/j.ajtas.20200905.15,
  author = {Samuel Olorunfemi Adams and Yahaya Haruna Umar},
  title = {Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {219-227},
  doi = {10.11648/j.ajtas.20200905.15},
  url = {https://doi.org/10.11648/j.ajtas.20200905.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.15},
  abstract = {Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.},
 year = {2020}
}

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TY  - JOUR
T1  - Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations
AU  - Samuel Olorunfemi Adams
AU  - Yahaya Haruna Umar
Y1  - 2020/10/12
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.15
DO  - 10.11648/j.ajtas.20200905.15
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  - 219
EP  - 227
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.15
AB  - Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.
VL  - 9
IS  - 5
ER  -

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Author Information

Samuel Olorunfemi Adams

Department of Statistics, University of Abuja, Abuja, Nigeria
Yahaya Haruna Umar

Department of Statistics, University of Abuja, Abuja, Nigeria

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APA Style

Samuel Olorunfemi Adams, Yahaya Haruna Umar. (2020). Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. American Journal of Theoretical and Applied Statistics, 9(5), 219-227. https://doi.org/10.11648/j.ajtas.20200905.15

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ACS Style

Samuel Olorunfemi Adams; Yahaya Haruna Umar. Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. Am. J. Theor. Appl. Stat. 2020, 9(5), 219-227. doi: 10.11648/j.ajtas.20200905.15

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AMA Style

Samuel Olorunfemi Adams, Yahaya Haruna Umar. Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations. Am J Theor Appl Stat. 2020;9(5):219-227. doi: 10.11648/j.ajtas.20200905.15

Copy | Download

@article{10.11648/j.ajtas.20200905.15,
  author = {Samuel Olorunfemi Adams and Yahaya Haruna Umar},
  title = {Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {219-227},
  doi = {10.11648/j.ajtas.20200905.15},
  url = {https://doi.org/10.11648/j.ajtas.20200905.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.15},
  abstract = {Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations
AU  - Samuel Olorunfemi Adams
AU  - Yahaya Haruna Umar
Y1  - 2020/10/12
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.15
DO  - 10.11648/j.ajtas.20200905.15
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  - 219
EP  - 227
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.15
AB  - Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.
VL  - 9
IS  - 5
ER  -

Copy | Download