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

Abstract

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