Comparison of Time Series Models before and after Using Wavelet Shrinkage Filtering to Forecast the Amount of Natural Gas in Iraq

Keywords: Time series, ARIMA, ACF, PACF, wavelets, akaike information criterion, schwarz bayesian information criterion, HQC


The procedure of reducing noise or reduction before analyzing the time series is important to get accurate and reliable outcomes when building models. Wavelet Shrinkage consisting of wavelets with thresholding is a powerful mathematical method used to reduce noise that can be exposed. It has time-series observations and selects the cut-off threshold level to be suitable for removing most noise. In this paper, natural gas production data in Iraq were used during (1981-2019), which included non-stationary data or outliers, so the researcher must treat this problem before starting the analysis. Thus, the researcher selected the way of time series analysis using Box- Jenkins (ARIMA (p,d,q) models and the method of wavelet shrinkage in the two methods of cutting the threshold before and after filtering wavelet shrinkage to choose the most suitable mathematical model that defines the study data. The paper was concerned with finding an efficient model by comparing the (Box-Jenkins) linear ARIMA (p, d, q) models estimated from the time series data before and after filtering the wavelet shrinkage, and then decreasing the rank of the estimated model from the candidate observations (While maintaining the accuracy and suitability of the estimated models) and re-comparing it with the estimated linear models of the original observations, and then measuring the most efficient model based on some statistical criteria, including the AIC (Akaike information criterion), SBIC (Schwarz information criterion, Bayesian information criterion BIC)and HQIC (Hannan-Quinn information criterion). Statistical programs such as Statgraphics XVII - X64 and MATLAB were used to analyze the data. The paper reached the efficiency of wavelet shrinkage filters in treating the noise problem and getting efficient estimated models, specifically the wavelet shrinkage filter (Daubechies(db8)) with a soft-threshold cut-off estimated by the fixed-form method, and the possibility of obtaining linear models with lower orders and higher efficiency for the filtered observations compared to the corresponding models estimated from the original observations, that is, the suitable model for the data is a model ARIMA(0,1,1) for the data paved in a Daubechies method, i.e., it is preferable to do the waveform analysis of the data before analyzing the time series concerning the observations of natural gas production in Iraq The preference was given to the model estimated by Box and Jenkins  ARIMA (0,1,1) model using wavelet shrinkage. Daubechies (db8) wavelet reduction


Download data is not yet available.


M. M. Ali, M. Z. Babai, J. Boylan and A. A. Syntetos. Supply chain forecasting when information is not shared. European Journal of Operational Research, vol. 260, no. 3, pp. 984-994, 2017.

S. E. Hikichi, E. G. Salgado and L. A. Beijo. Forecasting number of ISO 14001 certifications in the Americas using ARIMA models. Journal of Cleaner Production, vol. 147, pp. 242-253, 2017.

A. W. Omer, H. T. A. Blbas and D. H. Kadir. A comparison between brown’s and holt’s double exponential smoothing for forecasting applied generation electrical energies in Kurdistan region. Cihan University-Erbil Scientific Journal (CUESJ), vol. 5, no. 2, pp. 56-63, 2021.

D. H. Kadir. Time series modeling to forecast on consuming electricity. Journal of Al Rafidain University College, vol. 2020, no. 46, pp. 473-485, 2020.

H. R. Wang, C. Wang, X. Lin and J. Kang. An improved ARIMA model for hydrological simulations. Nonlinear processes in geophysics discussions. Nonlinear Processes in Geophysics Discussions, vol. 1, no. 1, pp. 841-876, 2014.

K. W. Wang, C. Deng, J. P. Li, Y. Y. Zhang, X. Y. Li and M. C. Wu. Hybrid methodology for tuberculosis incidence time-series forecasting based on ARIMA and a NAR neural network. Epidemiol Infect, vol. 145, p. 1118-1129, 2017.

D. L. Fugal. Conceptual Wavelets in Digital Signal Processing. San Diego, California: Space and Signals Technical Publishing, 2009.

A. S. Hamad. Using some Thresholding Rules in Waveletshrinkage to Denoise Signals for Simple Regression Withapplic Ation in Rezgary Hospital. Sulaimaniyah, Iraq: University of Sulaimani-College of Administration and Economics, 2010.

L. Xu, D. Zhang and K. Wang. Wavelet-based cascaded adaptive filter for removing baseline drift in pulse waveforms. IEEE Transactions on Biomedical Engineering, vol. 52, no. 11, pp. 1973-1975, 2005.

S. A. Broughton and K. Bryan. Discrete Fourier Analysis and Wavelets. United States: John Wiley & Sons, 2009.

C. S. Burrus, R. A. Gopinath and H. T. Guo. Introduction to Wavelets and Wavelet Transforms. United States: Prentice Hall, 1998.

P. Bloomfield. Fourier Analysis of Time Series: An Introduction. 2nd ed. United States: John Wiley & Sons, 2013.

I. L. Cascio. Wavelet Analysis and Denoising: New Tools for Economists. London, UK: Queen Mary College, 2007.

C. K. Chui. Wavelets: A Tutorial in Theory and Applications. San Diego, United State: Academic Press Professional, 1992.

I. Daubechies. Ten Lectures on Wavelets. United States: Society for Industrial and Applied Mathematics, 1992.

F. W. Elliott, D. J. Horntrop and A. J. Majda. A Fourier-Wavelet monte carlo method for fractal random fields. Journal of Computational Physics, vol. 132, no. 2, pp. 384-408, 1997.

S. Abbasion, A. Rafsanjani, A. Farshidianfar and N. Irani. Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine. Mechanical Systems and Signal Processing, vol. 21, no. 7, pp. 2933-2945, 2007.

H. Y. Gao and A. G. Bruce. Waveshrink with Firm Shrinkage. Statistica Sinica, vol. 7, pp. 855-874, 1997.

J. Kovacevic and W. Sweldens. Wavelet families of increasing order in arbitrary dimensions. IEEE Transactions on Image Processing, vol. 9, no. 3, pp. 480-496, 2000.

Comparing Fitted Models using the SIC, HQIC or AIC Information Criteria. Vose. Available from: [Last accessed on 2022 Jan 01].

How to Cite
Faqe Hussein M. Comparison of Time Series Models before and after Using Wavelet Shrinkage Filtering to Forecast the Amount of Natural Gas in Iraq. cuesj [Internet]. 30Mar.2022 [cited 28May2022];6(1):32-6. Available from:
Research Article