Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)

Aideyan Donald Osaro; Usman Suleiman

doi:doi:10.11648/j.pamj.20221102.12

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Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)

Aideyan Donald Osaro, Usman Suleiman

Published in Pure and Applied Mathematics Journal (Volume 11, Issue 2)

Received: 12 February 2022 Accepted: 3 March 2022 Published: 7 May 2022

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Abstract

In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes (1989-2010). The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the ‘best model’ for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the ‘best model’.

Published in	Pure and Applied Mathematics Journal (Volume 11, Issue 2)
DOI	10.11648/j.pamj.20221102.12
Page(s)	33-38
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

Aberrant, Resolution, Stock, Indexes, Decomposition

References

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[2]	Aideyan D. O. (2016). Time Series Analysis of Nigeria Gross Domestic Product Using US Dollar and British Pounds From 2000 – 2014. International Journal of Scientific and Engineering Research. (IJSER) ISSN: 2229-5518. Vol. 7, Issue 6, June 2016 Edition.
[3]	Barnet, V. & Lewis, T. (1994), outliers in statistical data, john Wiley, ISBN 0-471-93094-6, chichester.
[4]	Bilen, C., Huzurbazar, S. (2002), “wavelet-Based Detection of outliers in Time series”, journal of computational and Graphical statistics, volume 11, number 2, 311-327.
[5]	Donoho, D. L., I. M. Johnstone, G. Kerkyacharian, and D. Picard, 1993, April, Density estimation by wavelet thresholding, preprint, Department of statistics, Stanford university.
[6]	Eckley, I. A. (2001). Wavelet methods for Time Series and Spatial Data. Ph.D. Thesis, University of Bristol, U.K.
[7]	Grubbs, F. E. (1969), procedure for detecting outlying observations in samples, Technometrics 11, pp. 1-21.
[8]	Haar, A. (1910). ZurTheorie der orthogonal unktionen systeme. Math. Ann., 69, 331–371.
[9]	Hodge, V. J (2004), A survey of outlier detection methodologies, Kluver Academic Publishers, Netherlands January 2004.
[10]	Kantardzic, M. (2003). Data mining Concepts, Models, Methods and Algorithms. IEEE Transactions on neutral networks, VOL. 14, N. 2, March 2003.
[11]	Pereival, D. B. and Wadden, A. T. (2000). Wavelet Method for Time Series Analysis, Cambridge University Press, Cambridge.
[12]	Ramasmawy R.; Rastogi R. & Kyuseok S. (2000). Efficient algorithms for miningoutliers from large data sets. Proceedings of the ACM SIGMOD international Conference on management of data, pp. 427-438, ISBN 1-58113-217-4, Dallas, Texas, United states.
[13]	Sameh El-Sharo, Amani Al-Ghraibah, Jamal Al-Nabulsi, Mustafa Muhammad Matalgah (2020). Evaluation of the carotid artery using wavelet-based analysis of the pulse wave signal. International Journal of Electrical and Computer Engineering (IJECE) 10.11591/ijece.v12i2.pp1456-1467.
[14]	Saravanan S., Sujitha Juliet (2022) A Metaheuristic Approach for Tetrolet-Based Medical Image Compression Journal of Cases on Information Technology 10.4018/jcit.20220401.oa3. Vol 24 (2). pp. 1-14.
[15]	Shittu O. I and Aideyan D. O (2014): Wavelet Method of Detecting and Modeling Anomalous Observation in Gaussian and Non-Gaussian distributions. Published in International Journal of Scientific and Engineering Research. (IJSER) ISSN: 2229-5518. Vol. 5, Issue 12th Edition.
[16]	Tian-Xiao He and Tung Nguyen (2020) Wavelet Analysis and Applications in Economics and Finance. Research & Reviews: Journal of Statistics and Mathematical Sciences.

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APA Style

Aideyan Donald Osaro, Usman Suleiman. (2022). Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure and Applied Mathematics Journal, 11(2), 33-38. https://doi.org/10.11648/j.pamj.20221102.12

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ACS Style

Aideyan Donald Osaro; Usman Suleiman. Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure Appl. Math. J. 2022, 11(2), 33-38. doi: 10.11648/j.pamj.20221102.12

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Aideyan Donald Osaro, Usman Suleiman. Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure Appl Math J. 2022;11(2):33-38. doi: 10.11648/j.pamj.20221102.12

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@article{10.11648/j.pamj.20221102.12,
  author = {Aideyan Donald Osaro and Usman Suleiman},
  title = {Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {2},
  pages = {33-38},
  doi = {10.11648/j.pamj.20221102.12},
  url = {https://doi.org/10.11648/j.pamj.20221102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221102.12},
  abstract = {In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes (1989-2010). The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the ‘best model’ for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the ‘best model’.},
 year = {2022}
}

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TY  - JOUR
T1  - Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)
AU  - Aideyan Donald Osaro
AU  - Usman Suleiman
Y1  - 2022/05/07
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221102.12
DO  - 10.11648/j.pamj.20221102.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 33
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221102.12
AB  - In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes (1989-2010). The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the ‘best model’ for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the ‘best model’.
VL  - 11
IS  - 2
ER  -

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Author Information

Aideyan Donald Osaro

Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria
Usman Suleiman

Department of Mathematical Sciences, Kogi State University, Ayingba, Nigeria

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APA Style

Aideyan Donald Osaro, Usman Suleiman. (2022). Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure and Applied Mathematics Journal, 11(2), 33-38. https://doi.org/10.11648/j.pamj.20221102.12

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ACS Style

Aideyan Donald Osaro; Usman Suleiman. Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure Appl. Math. J. 2022, 11(2), 33-38. doi: 10.11648/j.pamj.20221102.12

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AMA Style

Aideyan Donald Osaro, Usman Suleiman. Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market). Pure Appl Math J. 2022;11(2):33-38. doi: 10.11648/j.pamj.20221102.12

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@article{10.11648/j.pamj.20221102.12,
  author = {Aideyan Donald Osaro and Usman Suleiman},
  title = {Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)},
  journal = {Pure and Applied Mathematics Journal},
  volume = {11},
  number = {2},
  pages = {33-38},
  doi = {10.11648/j.pamj.20221102.12},
  url = {https://doi.org/10.11648/j.pamj.20221102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221102.12},
  abstract = {In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes (1989-2010). The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the ‘best model’ for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the ‘best model’.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)
AU  - Aideyan Donald Osaro
AU  - Usman Suleiman
Y1  - 2022/05/07
PY  - 2022
N1  - https://doi.org/10.11648/j.pamj.20221102.12
DO  - 10.11648/j.pamj.20221102.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 33
EP  - 38
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20221102.12
AB  - In recent years the method of wavelet analysis has been opened to researchers. It is the analyses of data at different level of decomposition and can capture the characteristics of data series in all decomposition level. In this research work, data was collected on the Nigerian stock index for All Share and Capital market indexes (1989-2010). The data were analyzed by wavelet method to detect the aberrant observations (AOs) over the period under study for the two indexes. Akaike information criterion (AIC) was also used to detect the ‘best model’ for the two indexes using some distributions. A total of seventeen and eleven AOs were detected from the original data collected on All Share and Capital Market indexes respectively. In the first, second and third resolutions, a total of four, two and two AOs were detected from the All Share index, while a total of five, four and three AOs were detected from that of Capital Market index. The results obtained showed the AOs detected in the analysis of the original data maintain the same or closely the same positions as that obtained from the analysis of the decomposed data for the two stock indexes. It was observed that the index of stocks in March, July and December are more and less in February, March, and November for the two indexes. The AIC results show that, the Cauchy distribution has the smallest AIC values among the distributions used, which means is the ‘best model’.
VL  - 11
IS  - 2
ER  -

Copy | Download