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

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
[1] Stheim, D. (1994). Nonlinear Time Series, A Selective Review, Scandinavian Journal of Statistics, 21: 97-130.
[2] Diggle, P. J. and Hutchinson, M. F. (1989). On Spline Smoothing with Autocorrelated Errors, Australian Journal of Statistics, 31: 166-182.
[3] Kohn, R., Ansley, C. F., and Wong, C. (1992), ‘Nonparametric Spline Regression with Autoregressive Moving Average Errors,’ Biometrika, 79: 44-50.
[4] Hurvich, C. M., and Zeger, S. L. (1990). A Frequency Domain Selection Criterion for Regression with Autocorrelated Errors. Journal of the American Statistical Association. 85: 705-714.
[5] Yuedong, W. (2011). Smoothing Spline: Methods and Applications. Technometrics. 54 (3): 324-326. Chen, C. S. and Huang H. C. (2011): An improved Cp criterion for spline smoothing. Journal of Statistical Planning and Inference, 144 (1): 445-471.
[6] Reinsch, C. H. (1967). Smoothing by Spline Functions. Numer. Math. 10: 177–183.
[7] Craven, P., Wahba, G. (1979). Smoothing Noisy Data with Spline Functions. Numer. Math. 31: 377–403.
[8] Hutchinson, M. F., de Hoog, F. R. (1985): Smoothing Noisy Data with Spline Functions. Numer. Math., 47: 99–106.
[9] Golub, G. H., Heath, M., Wahba, G (1979). Generalized Cross-Validation as a Method for Choosing a Good Ridge, 21 (2): 215-223.
[10] Wahba, G. (1990). Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics. 59, Philadelphia: SIAM. 1-180.
[11] Hurvich, C. M., Simonoff, J. S. and Tsai, C. (1998). Smoothing Parameter Selection in Non-Parametric Regression using an Improved Akaike Information Criterion. Journal of Royal Statistical Society, B, 60 (2): 271-293.
[12] Gu, C. (1992). Diagnostic for Nonparametric Regression Models with Additive Term. Journal of American Statistical Association. 87 (420): 1051-1058.
[13] Yuedong, W. (1998). Smoothing Spline Models with Correlated Random Errors. Journal of American Statistical Association. (93) 441: 341-348.
[14] Devi, A. R., Budiantara, I. N. and Vita Ratnasari, V. (2018). Unbiased Risk and Cross-Validation Method for Selecting Optimal Knots in Multivariable Nonparametric Regression Spline Truncated (case study: the Unemployment rate in Central Java, Indonesia, 2015). AIP Conference Proceedings 2021.
[15] Anna L., Tong, T. and Yuedong W. (2006). Smoothing Spline Estimation of Variance Function. Journal of Computational and Graphical Statistics 16 (2): 1-10.
[16] Aydin, D and Tuzemen, S. (2012). Smoothing Parameter Selection Problem in Nonparametric Regression Based on Smoothing Spline: A Simulation Study. Journal of Applied Sciences. 12 (7): 636-644.
[17] Aydin, D. and Memmedli, M. (2011). Optimum Smoothing Parameter Selection for Penalized Least squares inform of Linear Mixed Effect Models. Optimization, iFirst: 1–18.
[18] Chen, C. S. and Huang H. C. (2011): An improved Cp criterion for spline smoothing. Journal of Statistical Planning and Inference, 144 (1): 445-471.
[19] Aydin, D., M. Memmedli, and R. E. Omay. (2013). Smoothing Parameter Selection for Nonparametric Regression using Smoothing Spline. European Journal of Pure and Applied Mathematics. 6: 222–38.
[20] Jansen J. P. and Vieira, M. C. and Cope S. (2015). Network Meta-Analysis of Longitudinal Data Using Fractional Polynomials. Statistics in Medicine, 34 (15).
[21] Adams S. O. and Ipinyomi R. A. (2017). A Proposed Spline Smoothing Estimation Method for Time Series Observations. International Journal of Mathematics and Statistics Invention (IJMSI). 7 (2): 18-25.
[22] Xu, L and Zhou J. (2019). A Model-Averaging Approach for Smoothing Spline Regression. Communications in Statistics - Simulation and Computation. 48 (8): 2438-2451.
[23] Wahba, G. (1977). Applications of Statistics, in P. Krishnaiah (ed.), A Survey of Some Smoothing Problems and the Method of Generalized Cross-Validation for solving them, Northern Holland, Amsterdam. 14 (4): 651-667.
[24] Wahba, G. (1980). Automatic Smoothing of the Log Periodogram. Journal of the American Statistical Association 75: 122-132.
[25] Wahba, G., and Wang, Y. (1993). Behavior near Zero of the Distribution of GCV Smoothing Parameter Estimates for Splines. Statistics and Probability Letters. 25: 105-111.
[26] Mallows, C. L., (1973). Some Comments on Cp, Technometrics, 15 (4), 661-675.
[27] Wahba, G., Wang, Y., Gu, C., Klein, R., and KIein, B. (1995). Smoothing Spline ANOVA for Exponential Families, With Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy. The Annals of Statistics, 23, 1865-1895.
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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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    T1  - Comparative Study of GCV-MCP Hybrid Smoothing Methods for Predicting Time Series Observations
    AU  - Samuel Olorunfemi Adams
    AU  - Yahaya Haruna Umar
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    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
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    PB  - Science Publishing Group
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    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
  • Department of Statistics, University of Abuja, Abuja, Nigeria

  • Department of Statistics, University of Abuja, Abuja, Nigeria

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