Forecasting Time Series Data Using Haar Discrete Wavelet Transformation


  • Hartina Husain IAIN Parepare
  • Amran Amran



Discrete Wavelet Transform, Fourier Transform, Haar Wavelet, Periodogram, Fisher's Test


Discrete Wavelet Transform is a data transformation method that represents data in the time domain and frequency domain. This transformation appears to overcome the weakness of the Fourier transform which is only able to provide one domain information and is limited to certain windowing . The type of wavelet used is the Haar Wavelet. Identification of data periodicity using Periodogram analysis with Fisher's Test statistics. The transformed data is decomposed into two components, namely the Approximation Coefficient and the Detail Coefficient. Both components are predicted using the Box-Jenkins ARIMA method. Model selection was carried out using the Akaike Information Criterion (AIC ) and Mean Square Error (MSE) methods . The forecast obtained is then reconstructed into the time domain (inverse). The application of the ARIMA model through wavelet transformation to Makassar City Air Humidity data for the period September 2006 - December 2012 shows that forecasting on the Approximation Coefficient obtained by the ARIMA model (0,0,3) with AIC = 112.2142 and MSE = 29.673. While forecasting on Detailed Coefficients is obtained by the ARIMA model (2,1,0) with AIC = 89.2 and MSE = 15,989.


Download data is not yet available.


Aditya Satrio, C. B., Darmawan, W. B., Nadia, U. and Hanafiah, N. 2020. Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET,” Procedia Comput. Sci., vol. 179, no. pp. 524–532, 2021, doi: 10.1016/j.procs.2021.01.036.

Amin, R. , Shah, K., Asif, M., Khan, I. and Ullah, F. 2020. An efficient algorithm for numerical solution of fractional integro-differential equations via Haar wavelet. J. Comput. Appl. Math., vol. 381, p. 113028, doi: 10.1016/

Apelgren, P. et al., 2019. Study of wavelet-based denoising and a new shrinkage function for low-dose CT Scans. Mater. Today Proc., vol. 27, no. xxxx, pp. 0–31, [Online].

Burrus et al, C. S. . 1998. Introduction to Wavelets and Wavelet Transforms a Primer. United State of America: Prentice Hall.

Daubechies, I. , 1992. Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics. SIAM.

Friadi, R. and Junadhi, J. 2019. Sistem Kontrol Intensitas Cahaya, Suhu dan Kelembaban Udara Pada Greenhouse Berbasis Raspberry PI. J. Technopreneursh. Inf. Syst., vol. 2, no. 1, pp. 30–37, doi: 10.36085/jtis.v2i1.217.

Guo, T., Zhang, T., Lim, E., Lopez-Benitez, M., Ma, F. and Yu, L., 2022. A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities. IEEE Access, vol. 10, pp. 58869–58903, doi: 10.1109/ACCESS.2022.3179517.

Katsavrias, C., Papadimitriou, C., Hillaris, A. and Balasis, G., 2022. Application of Wavelet Methods in the Investigation of Geospace Disturbances: A Review and an Evaluation of the Approach for Quantifying Wavelet Power. Atmosphere (Basel)., vol. 13, no. 3, doi: 10.3390/atmos13030499.

Khan, S. and Alghulaiakh, H., 2020. ARIMA model for accurate time series stocks forecasting. Int. J. Adv. Comput. Sci. Appl., vol. 11, no. 7, pp. 524–528, doi: 10.14569/IJACSA.2020.0110765.

Lim, B. and Zohren, S.,2021. Time-series forecasting with deep learning: A survey. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 379, no. 2194, doi: 10.1098/rsta.2020.0209.

Olsavszky,V., Dosius, M., Benecke, J., and Vladescu, C., 2020. Time series analysis and forecasting with automated machine learning on a national ICD-10 database. Int. J. Environ. Res. Public Health, vol. 17, no. 14, pp. 1–17, doi: 10.3390/ijerph17144979.

Othman, G. and Zeebaree, D.Q., 2020. The Applications of Discrete Wavelet Transform in Image Processing: A Review. J. Soft Comput. Data Min., vol. 1, no. 2, pp. 31–43, [Online].

Rhif, M., Ben Abbes, A., Farah, I. R., Martínez, B. and Sang, Y., 2019. Wavelet transform application for/in non-stationary time-series analysis: A review. Appl. Sci., vol. 9, no. 7, pp. 1–22, doi: 10.3390/app9071345.

Solichin,Z., 2011. Program Aplikasi Keamanan Citra Dengan Algoritma Des dan Transformasi Wavelet Diskrit. [Online].

WAHYUNI, N. P. M. S., SUMARJAYA, I. W. and SRINADI, I. G. A. M. 2016. 2016. Peramalan Curah Hujan Menggunakan Metode Analisis Spektral. E-Jurnal Mat., vol. 5, no. 4, p. 183, doi: 10.24843/mtk.2016.v05.i04.p139.

Wei, W. W., 1994. Time Series Analysis Univariate and Multivariate Methods. California: Addison-Wesley Publishing Company.




How to Cite

Husain, H., & Amran, A. (2023). Forecasting Time Series Data Using Haar Discrete Wavelet Transformation. Jurnal Matematika, Statistika Dan Komputasi, 19(3), 484-497.



Research Articles