A Proposed Wavelet and Forecasting Wind Speed with Application

Article Sidebar

PDF
Published: Apr 20, 2023
DOI: https://doi.org/10.30526/36.2.3060
Keywords:
ARIMA, Fibonacci Coefficient Polynomials, Proposed Wavelet, Time Series, Wavelet Transform.

Main Article Content

Layla A. Ahmed
Department of Statistics and Informatics, College of Administration and Economics, University of Sulaimani, Kurdistan Region
Monem Mohammed
Department of Statistics and Informatics, College of Administration and Economics, University of Sulaimani, Kurdistan Region, Iraq

Abstract

Time series analysis is the statistical approach used to analyze a series of data. Time series is the most popular statistical method for forecasting, which is widely used in several statistical and economic applications. The wavelet transform is a powerful mathematical technique that converts an analyzed signal into a time-frequency representation. The wavelet transform method provides signal information in both the time domain and frequency domain. The aims of this study are to propose a wavelet function by derivation of a quotient from two different Fibonacci coefficient polynomials, as well as a comparison between ARIMA and wavelet-ARIMA. The time series data for daily wind speed is used for this study. From the obtained results, the proposed wavelet-ARIMA is the most appropriate wavelet for wind speed. As compared to wavelets the proposed wavelet is the most appropriate wavelet for wind speed forecasting, it gives us less value of MAE and RMSE.

Article Details

How to Cite
[1]
Layla A. Ahmed and Mohammed, M. 2023. A Proposed Wavelet and Forecasting Wind Speed with Application . Ibn AL-Haitham Journal For Pure and Applied Sciences. 36, 2 (Apr. 2023), 420–429. DOI:https://doi.org/10.30526/36.2.3060.
Issue
Vol. 36 No. 2 (2023)
Section
Mathematics
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

licenseTerms
Crossref
Scopus
Google Scholar
Europe PMC

Publication Dates

References

Milon, M. H. Comparison on Fourier and Wavelet Transformation for an ECG Signal. American Journal of Engineering Research. 2017, 6, 8, 1-7.

Meng, L. T. Wavelet-based Multi-resoulation Techniques for Two-dimension Data Analysis, master thesis, University of London England, 1997.

Mehra, M.; Behera, R. Applications and Properties of Different Kind of Wavelet. Indian Journal of Industrial and Applied Mathematics. 2013, 4, 1, 1-15.

Patel, Y.; Deb, D. Machine Inelligent Hybrid Methods based on Kalman Filter and Wavelet Transform for Short Term Wind Speed Prediction, Wind, 2022, 2, 37-50.

Yaacob, N. A.; Jabar, J. J.; Pathmanathan, D.; Alwadi, S.; Mohamed, I. Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates, Mathematics, 2021, 9, 2295, 1-11.

Mandrikova, O.; Fatisova, N.; Polozov, Y. Hybrid model for Time Series of Complex Structure with ARIMA Components. Mathematics, 2021, 9, 1122, 1-19.

Babu, R.; Pachiyappan, A. Improving Forecast Accuracy of Wind Speed Using Wavelet Transform and Neural Networks. Journal of Electrical Engineering and Technology, 2013, 8, 3, 559-564.

Ramana, R.V.; Krishna, B.; Kumar S. R.; Pandey, N. G. Monthly Rainfall Prediction Using Wavelet Neural Network Analysis. Water Resource Manage, 2013, 27, 3697-3711.

Al Wadi, S.; Hamarsheh, A. and Alwadi, H. Maximum Overlapping Discrete Wavelet Transform in Forecasting Banking Sector. Applied Mathematical Sciences, 2013, 7, 8, 3995-4002.

Chandra, D. R.; Kumari, M. S.; Sydulu, M.; Grimaccia, F.; Mussetta, M. Adaptive Wavelet Neural Network Based Wind Speed Forecasting Studies. Electr Eng Technol, 2014, 9, 6, 1812-1821.

Kumar, J.; Kaur, A.; Manchanda, P. Forecasting the Time Series Data Using ARIMA with Wavelet. Journal of Computer and Mathematical Sciences, 2015, 6, 8, 430-438.

Ji, F.; X. Cai, X.; Zhang, J. Wind power prediction interval estimation method using wavelet transform neuro-fuzzy network. Journal of Intelligent and Fuzzy Systems, 2015, 29, 6, 2439-2445.

Alvarado, F. V.; Oliveira, B. R.; Duarte, Q.; Lamblem, R. A Wavelet Generated from Fibonacci Coefficient Polynomials and its Application in Carbiac arrhythmia Classification. National meeting computational modeling and VII ECTM-meeting on materials science and technology, Joao Pessoa, 2016, 19-21.

Sang, Y.; Singh, V.; Sun, F.; Chen, Y. Wavelet-Based Hydrological Time Series Forecasting. Journal of Hydrologic Engendering, 2016, 21, 5.

Saini,S. Ahuja, M. Wind Speed Prediction Using Wavelet transform and Artificial Neural Network. IJRECE, 2017, 5, 4, 161-168.

Bunrit, S.; Kerdprasop, N.; Kerdprasop, K. Multiresolution Analysis Based on Wavelet Transform for Commodity Prices Time Series Forecasting. International Journal of Machine Learning and Computing, 2018, 8, 2, 175-180.

Gossler, F.; Oliveira, B.; Filho, J.; Alvarado,F.; Duarte, M. and Lamblem, R. A Comparative Study between Mexican and Golden Hat Wavelets. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018, 6, 2, 1-7.

Gossler, F.; Oliveira, B.; Filho, J.; Alvarado, F.; Lamblem, R. Gaussian and Golden Wavelets: A Comparative Study and their Applications in Structural Health Monitoring. Trends in Computational and Applied Mathematics, 2021, 22, 1, 139-155.

John, E. E.; Patric, U. U. Short- Term Forecasting of Nigeria Inflation Rates Using Seasonal ARIMA Model. Science Journal of Applied Mathematics and Statistics, 2016, 4, 3, 101-107.

Ergen,B. Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds. Journal of Signal and Information Processing, 2013, 4, 164-167.

Borowska, M.; Bialoblocka, N. Multiresolution Analysis of EEG Signals, studies in logic. Grammar and rhetoric, 2016, 47, 60, 21-31.

Yih Kuo, J.; Yi You, S.; Chi Lin, H.; Yang Hsu, C.; Lei, B. Constructing condition Monitoring Model of Wind Turbine Blades. Mathematics, 2022, 10, 972, 1-13.

Shi, M.; Yu, H.; Wang, H. Automated Detection of sudden Cardiac Death by Discrete Wavelet Transform of Electrocardiogram Signal. Symmetry, 2022, 14, 571, 1-14.

Stepanov, A. Polynomial, Neural Network, and Spline Wavelet Models for Continuous Wavelet Transform of Signals. Sensors, 2021, 21, 6416, 1-16.

Arora, S.; Brar, Y. S.; Kumar, Sh. Haar Wavelet Transformation of Image Retrieval. International Journal of Advanced Computer and Mathematical Sciences, 2014, 5, 2, 27-31.

Ahmed, M. A.; Taha, H. A.; Aldeen, M. T. Image Compression using Haar and Modified Haar Wavelet Transform. Tikrit Journal of Eng. Sciences, 2011, 18, 2, 88-101.

Shaker, A. N. Comparison between Orthogonal and Bi-orthogonal Wavelets. Journal of Southwest Jiao Tong University, 2020, 55, 2, 1-10.

Nury, A.; Hasan, K.; Alam, J. Comparative study of wavelet-ARIMA and wavelet-ANN models for temperature time series data in northeastern Bangladesh. Journal of King Saud University-Science, 2015.

Nali, A.; Haukkanen, P. On Generalized Fibonacci and Lucas Polynomials. Chaos Solitons and Fractals, 2009, 42, 3179-3186.

Ozkan, E; Tastan,M. 2- Fibonacci Polynomials in the Family of Fibonacci Numbers. Notes on number theory and discrete mathematics, 2018, 24, 3, 47-55.

Boonyarak, J. On Polynomials Generated by the Hyper- Fibonacci Numbers. Master thesis, University of Burapha, 2020.