A NEW APPROACH FOR MODELLING SKEWED-SEASONAL TIME SERIES DATASETS
Keywords:
Skewed-Seasonal Model (SSM), Autoregressive Model, Durbin Watson, Autocorrelation function (ACF), Partial Autocorrelation function (PACF)
Abstract
New models applicable to skewed distributions have been developed since the transformation changes the structure of the original series. These models fail when applied to datasets that exhibit seasonality and skewness, as accurately modeling the data structure aids in forecasting and planning. The study proposed the Skewed-Seasonal Model (SSM) for the simulated data. The results showed that the proposed Skewed-Seasonal Model (SSM) accounted for the variability in the series better than the AR model. The Skewed-Seasonal Model (SSM) approach exhibited better goodness of fit, in addition to higher forecasting ability than the AR model. The forecast evaluation metrics indicated that the forecast evaluation of the Skewed-Seasonal Model (SSM) had lower values, making the proposed Skewed-Seasonal Model (SSM) more effective than the standard Autoregressive model in capturing and predicting the behavior of skewed-seasonal time series.
References
[1] P. Malik, A. Dangi, A. Singh, T. Asst, A. Pratap, S. Parihar, U. Sharma, L. Mishra. An Analysis of Time Series Analysis and Forecasting Techniques. International Journal of Advanced Research in Computer and Communication Engineering; (2023). 9. https://doi.org/6.0415/IJARIIE-21608
[2] M. Kolambe. Forecasting the Future: A Comprehensive Review of Time Series Prediction Techniques. Journal of Electrical Systems; (2024). 20. 575-586. https://doi.org/10.52783/jes.1478.
[3] F. Jonas, A.D. Haderlein, A.N. Peterson, L. Burkitt, D.B. Mareels. Autoregressive models for biomedical signal processing; (2023). arXiv.Org, abs/2304.11070. https://doi.org/10.48550/arXiv.2304.11070
[4] Y. Liu, J. Wang, V. Leiva, A. Tapia, W. Tan, S. Liu. Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application. Journal of Applied Statistics; (2023). https://doi.org/10.1080/02664763.2023.2198178.
[5] P.C. Padhan. Application of ARIMA Model for Forecasting Agricultural Productivity in India. Journal of Agriculture and Social Science; 2012. 8(2), PP. 50-56. https://doi.org/11–017/AWB/2012/8–2–50–56.
[6] A. Choudhury, J. Jones. Crop Yield Prediction Using Time Series Models. Journal of Economics and Economic Education Research; (2014). 15(3), pp. 53.
[7] B. Fernandez, J. Salas. Gamma-autoregressive models for streamflow simulation. Journal of Hydraulic Engineering; 1990. 116, 1403–1414. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:11(140)
[8] A.F. Adedotun, A.I. Taiwo, T.O. Olatayo. A Re-parametrised Autoregressive Model for Modelling Gross Domestic Product. ANNALS of Faculty Engineering Hunedoara-International Journal of Engineering; (2020). 84-188 http://eprints.covenantuniversity.edu.ng/id/eprint/17549
[9] A.F. Adedotun, T.O. Olatayo, G.O. Odekina. On Non-Linear Non-Gaussian Autoregressive Model with Application to Daily Exchange Rate, Journal of Physics: Conference Series; (2022). https://doi.org/10.1088/1742-6596/2199/1/012031
[10] T.O. Olatayo, K. Ekerikevwe. Performance Measures for Evaluating the Accuracy of Time Series Hybrid Model Using High Frequency Data. Britain International of Exact Sciences (BIoEx); (2022). 4. 244-259. https://doi.org/10.33258/bioex.v4i3.760.
[11] T. F. Ribeiro, A. P. Alencar, F. M. Bayer, “Bivariate generalized autoregressive models for forecasting bivariate non-Gaussian times series”, (2025). Available: https://arxiv.org/pdf/2507.14442
[12] S.K. Padhee, S. Dutta. Spatio-temporal reconstruction of MODIS NDVI by regional land surface phenology and harmonic analysis of time-series. GIScience & Remote Sensing; (2019). 56 (8), 1261–1288. https://doi.org/10.1080/15481603.2019.1646977
[13] Q. Tarawneh. Harmonic analysis of precipitation climatology in Saudi Arabia. Theoretical Applied Climatology; (2016). 124: 205-217. https://doi.org/10.1007/s00704-015-1408-z
[14] J.O. Fantola, O.O Akanni. Forecasting COVID-19 Confirmed Cases: Time Series Analysis Perspective. The International Journal of Science & Technology; (2021). 9(5), doi:0.24940/theijst/2021/v9/i5/ST2105-015
[15] T.A. Lasisi, O.O Akanni. Time Series Modeling of Water Quality Parameters. Journal of Environmental and Earth Sciences. (2020). 10(9), 41-49, doi: 10.7176/JEES/10-9-07
[16] H. Van Loon, R.L. Jenne, K. Labitzke. Zonal Harmonic Standing Waves. Journal of Geophysical Research; 1973. 78: 4463-4471. https://doi.org/10.1029/JC078i021p04463
[17] F. Arabi, S. Shojaei, M. Zare, H.R.G. Malamiri. Investigating the capability of the Harmonic Analysis of Time Series (HANTS) algorithm in reconstructing time series images of daytime and nighttime land surface temperature from the MODIS sensor. Spat. Inf. Res. 32, 425–439 (2024). https://doi.org/10.1007/s41324-023-00569-3
[18] D.R. Legates, C.J. Willmott. Mean seasonal and spatial variability in gauge-corrected, global precipitation. International Journal of Climatology; (1990). 10(2): 111-127. http://dx.doi.org/10.1002/joc.3370100202
[19] Z. Qiang, Z. Zhu, G. Xian, C. Li. A novel regression method for harmonic analysis of time series. ISPRS Journal of Photogrammetry and Remote Sensing; (2022). 48-61. https://doi.org/10.1016/j.isprsjprs.2022.01.006
[20] T.A. Lasisi, O.O Akanni. Water Quality Parameters: Statistical Point of View, Journal of Natural Sciences Research. (2020). 10(9), 75-85, doi: 10.7176/JNSR/11-18-06
[21] D.O. Kofoworola, O.O Akanni, A.J. Solagbade. Knowledge and perceived benefits of telemedicine adoption and online medical consultation among healthcare professionals at Ade-Oyo Maternity Hospital, Ibadan, Oyo State. Electronic Journal of Medical and Educational Technologies. (2024). 17(1)
[22] S.A. Agboluaje, O.O. Akanni. M.U. Abdulrahman, M.G. Adelaja. Knowledge and Treatment Adherence Determinants among Tuberculosis Patients in Ibadan South West Local Government Area. Researchjournali’s Journal of Public Health. (2026). 12(1). 1-19
[23] H. Akaike. Information theory and an extension of maximum likelihood principle, Second International Symposium on Information Theory, Akademia Kiado. (1973). pp. 267–281.
[24] H. Akaike. A Bayesian analysis of the minimum AIC procedure. Annal Institute of Mathematical Statistics; (1978). A(30), 9–14.
[25] G.M. Ljung, G.E.P. Box. On a Measure of Lack of Fit in Time Series Models. Biometrika; 1978. 65(2), 297–303. https://doi.org/10.2307/2335207.
[26] T.O. Olatayo, A.I. Taiwo. Modeling and Evaluating Performances with Neural Network Using Climate Time Series Data. Nigerian Journal of Mathematics and Applications; (2016). 25; 205-216
[2] M. Kolambe. Forecasting the Future: A Comprehensive Review of Time Series Prediction Techniques. Journal of Electrical Systems; (2024). 20. 575-586. https://doi.org/10.52783/jes.1478.
[3] F. Jonas, A.D. Haderlein, A.N. Peterson, L. Burkitt, D.B. Mareels. Autoregressive models for biomedical signal processing; (2023). arXiv.Org, abs/2304.11070. https://doi.org/10.48550/arXiv.2304.11070
[4] Y. Liu, J. Wang, V. Leiva, A. Tapia, W. Tan, S. Liu. Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application. Journal of Applied Statistics; (2023). https://doi.org/10.1080/02664763.2023.2198178.
[5] P.C. Padhan. Application of ARIMA Model for Forecasting Agricultural Productivity in India. Journal of Agriculture and Social Science; 2012. 8(2), PP. 50-56. https://doi.org/11–017/AWB/2012/8–2–50–56.
[6] A. Choudhury, J. Jones. Crop Yield Prediction Using Time Series Models. Journal of Economics and Economic Education Research; (2014). 15(3), pp. 53.
[7] B. Fernandez, J. Salas. Gamma-autoregressive models for streamflow simulation. Journal of Hydraulic Engineering; 1990. 116, 1403–1414. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:11(140)
[8] A.F. Adedotun, A.I. Taiwo, T.O. Olatayo. A Re-parametrised Autoregressive Model for Modelling Gross Domestic Product. ANNALS of Faculty Engineering Hunedoara-International Journal of Engineering; (2020). 84-188 http://eprints.covenantuniversity.edu.ng/id/eprint/17549
[9] A.F. Adedotun, T.O. Olatayo, G.O. Odekina. On Non-Linear Non-Gaussian Autoregressive Model with Application to Daily Exchange Rate, Journal of Physics: Conference Series; (2022). https://doi.org/10.1088/1742-6596/2199/1/012031
[10] T.O. Olatayo, K. Ekerikevwe. Performance Measures for Evaluating the Accuracy of Time Series Hybrid Model Using High Frequency Data. Britain International of Exact Sciences (BIoEx); (2022). 4. 244-259. https://doi.org/10.33258/bioex.v4i3.760.
[11] T. F. Ribeiro, A. P. Alencar, F. M. Bayer, “Bivariate generalized autoregressive models for forecasting bivariate non-Gaussian times series”, (2025). Available: https://arxiv.org/pdf/2507.14442
[12] S.K. Padhee, S. Dutta. Spatio-temporal reconstruction of MODIS NDVI by regional land surface phenology and harmonic analysis of time-series. GIScience & Remote Sensing; (2019). 56 (8), 1261–1288. https://doi.org/10.1080/15481603.2019.1646977
[13] Q. Tarawneh. Harmonic analysis of precipitation climatology in Saudi Arabia. Theoretical Applied Climatology; (2016). 124: 205-217. https://doi.org/10.1007/s00704-015-1408-z
[14] J.O. Fantola, O.O Akanni. Forecasting COVID-19 Confirmed Cases: Time Series Analysis Perspective. The International Journal of Science & Technology; (2021). 9(5), doi:0.24940/theijst/2021/v9/i5/ST2105-015
[15] T.A. Lasisi, O.O Akanni. Time Series Modeling of Water Quality Parameters. Journal of Environmental and Earth Sciences. (2020). 10(9), 41-49, doi: 10.7176/JEES/10-9-07
[16] H. Van Loon, R.L. Jenne, K. Labitzke. Zonal Harmonic Standing Waves. Journal of Geophysical Research; 1973. 78: 4463-4471. https://doi.org/10.1029/JC078i021p04463
[17] F. Arabi, S. Shojaei, M. Zare, H.R.G. Malamiri. Investigating the capability of the Harmonic Analysis of Time Series (HANTS) algorithm in reconstructing time series images of daytime and nighttime land surface temperature from the MODIS sensor. Spat. Inf. Res. 32, 425–439 (2024). https://doi.org/10.1007/s41324-023-00569-3
[18] D.R. Legates, C.J. Willmott. Mean seasonal and spatial variability in gauge-corrected, global precipitation. International Journal of Climatology; (1990). 10(2): 111-127. http://dx.doi.org/10.1002/joc.3370100202
[19] Z. Qiang, Z. Zhu, G. Xian, C. Li. A novel regression method for harmonic analysis of time series. ISPRS Journal of Photogrammetry and Remote Sensing; (2022). 48-61. https://doi.org/10.1016/j.isprsjprs.2022.01.006
[20] T.A. Lasisi, O.O Akanni. Water Quality Parameters: Statistical Point of View, Journal of Natural Sciences Research. (2020). 10(9), 75-85, doi: 10.7176/JNSR/11-18-06
[21] D.O. Kofoworola, O.O Akanni, A.J. Solagbade. Knowledge and perceived benefits of telemedicine adoption and online medical consultation among healthcare professionals at Ade-Oyo Maternity Hospital, Ibadan, Oyo State. Electronic Journal of Medical and Educational Technologies. (2024). 17(1)
[22] S.A. Agboluaje, O.O. Akanni. M.U. Abdulrahman, M.G. Adelaja. Knowledge and Treatment Adherence Determinants among Tuberculosis Patients in Ibadan South West Local Government Area. Researchjournali’s Journal of Public Health. (2026). 12(1). 1-19
[23] H. Akaike. Information theory and an extension of maximum likelihood principle, Second International Symposium on Information Theory, Akademia Kiado. (1973). pp. 267–281.
[24] H. Akaike. A Bayesian analysis of the minimum AIC procedure. Annal Institute of Mathematical Statistics; (1978). A(30), 9–14.
[25] G.M. Ljung, G.E.P. Box. On a Measure of Lack of Fit in Time Series Models. Biometrika; 1978. 65(2), 297–303. https://doi.org/10.2307/2335207.
[26] T.O. Olatayo, A.I. Taiwo. Modeling and Evaluating Performances with Neural Network Using Climate Time Series Data. Nigerian Journal of Mathematics and Applications; (2016). 25; 205-216
Published
2026-04-16
How to Cite
AKANNI, O. O., OLATAYO , T. O., & TAIWO, A. I. (2026). A NEW APPROACH FOR MODELLING SKEWED-SEASONAL TIME SERIES DATASETS. Unilag Journal of Mathematics and Applications, 6(2), 20 - 30. Retrieved from https://lagjma.unilag.edu.ng/article/view/3035
Section
Articles
Copyright (c) 2026 OLUKUNMI OLATUNJI AKANNI, TIMOTHY OLABISI OLATAYO , ABASS ISHOLA TAIWO
This work is licensed under a Creative Commons Attribution 4.0 International License.
