Forecasting Time Series Data Using Haar Discrete Wavelet Transformation

Hartina Husain; Amran Amran

doi:10.20956/j.v19i3.24807

Authors

Hartina Husain IAIN Parepare
Amran Amran

DOI:

https://doi.org/10.20956/j.v19i3.24807

Keywords:

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

Abstract

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.

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