Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations

Poti Abaja Owili

doi:doi:10.11648/j.sjams.20150306.12

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Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations

Poti Abaja Owili

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)

Received: 4 October 2015 Accepted: 21 October 2015 Published: 30 October 2015

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Abstract

This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for bilinear time series models BL (1, 0, 1, 1) using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)
DOI	10.11648/j.sjams.20150306.12
Page(s)	234-242
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

Optimal Linear Interpolation, Simulation, MSE, Innovations, ANN, Exponential Smoothing

References

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Poti Abaja Owili. (2015). Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Science Journal of Applied Mathematics and Statistics, 3(6), 234-242. https://doi.org/10.11648/j.sjams.20150306.12

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Poti Abaja Owili. Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Sci. J. Appl. Math. Stat. 2015, 3(6), 234-242. doi: 10.11648/j.sjams.20150306.12

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AMA Style

Poti Abaja Owili. Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Sci J Appl Math Stat. 2015;3(6):234-242. doi: 10.11648/j.sjams.20150306.12

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@article{10.11648/j.sjams.20150306.12,
  author = {Poti Abaja Owili},
  title = {Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {6},
  pages = {234-242},
  doi = {10.11648/j.sjams.20150306.12},
  url = {https://doi.org/10.11648/j.sjams.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.12},
  abstract = {This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for bilinear time series models BL (1, 0, 1, 1) using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.},
 year = {2015}
}

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TY  - JOUR
T1  - Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations
AU  - Poti Abaja Owili
Y1  - 2015/10/30
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150306.12
DO  - 10.11648/j.sjams.20150306.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
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PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150306.12
AB  - This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for bilinear time series models BL (1, 0, 1, 1) using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.
VL  - 3
IS  - 6
ER  -

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Author Information

Poti Abaja Owili

Mathematics and Computer Science Department, Laikipia University, Nyahururu, Kenya

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APA Style

Poti Abaja Owili. (2015). Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Science Journal of Applied Mathematics and Statistics, 3(6), 234-242. https://doi.org/10.11648/j.sjams.20150306.12

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ACS Style

Poti Abaja Owili. Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Sci. J. Appl. Math. Stat. 2015, 3(6), 234-242. doi: 10.11648/j.sjams.20150306.12

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AMA Style

Poti Abaja Owili. Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations. Sci J Appl Math Stat. 2015;3(6):234-242. doi: 10.11648/j.sjams.20150306.12

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@article{10.11648/j.sjams.20150306.12,
  author = {Poti Abaja Owili},
  title = {Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {6},
  pages = {234-242},
  doi = {10.11648/j.sjams.20150306.12},
  url = {https://doi.org/10.11648/j.sjams.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.12},
  abstract = {This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for bilinear time series models BL (1, 0, 1, 1) using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Imputation of Missing Values for BL (P,0,P,P) Models with Normally Distributed Innovations
AU  - Poti Abaja Owili
Y1  - 2015/10/30
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150306.12
DO  - 10.11648/j.sjams.20150306.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 234
EP  - 242
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150306.12
AB  - This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for bilinear time series models BL (1, 0, 1, 1) using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.
VL  - 3
IS  - 6
ER  -

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