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Forecasting Time Series Data Using Haar Discrete Wavelet Transformation

PERAMALAN DATA DERET WAKTU MENGGUNAKAN TRANSFORMASI WAVELET DISKRIT HAAR

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 3 (2023) · pp. 484–497

DOI
10.20956/j.v19i3.24807
ISSN
2614-8811, 1858-1382
Published
2023-05-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

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.

Bahasa Indonesia

Transformasi Wavelet Diskrit merupakan metode transformasi data yang merepresentasikan data dalam domain waktu dan domain frekuensi. Transformasi ini muncul untuk mengatasi kelemahan transformasi Fourier yang hanya mampu memberikan satu informasi domain saja dan terbatas pada windowing tertentu. Jenis wavelet yang digunakan yaitu Wavelet Haar. Identifikasi keperiodikan data menggunakan analisis Periodogram dengan statistik Uji Fisher. Data hasil transformasi didekomposisi menjadi dua komponen yaitu koefisien Aproksimasi dan Koefisien Detail. Kedua komponen tersebut diramalkan menggunakan metode ARIMA Box-Jenkins. Pemilihan model dilakukan menggunakan metode Akaike Information Criterion (AIC) dan Mean Square Error (MSE). Peramalan yang diperoleh kemudian dikonstruksi kembali ke domain waktu (invers). Aplikasi model ARIMA melalui transformasi wavelet pada data Kelembaban Udara Kota Makassar periode September 2006 - Desember 2012 menunjukkan bahwa peramalan pada Koefisien Aproksimasi diperoleh model ARIMA (0,0,3) dengan nilai AIC = 112.2142 dan MSE=29.673. Sementara peramalan pada Koefisien Detail diperoleh model ARIMA (2,1,0) dengan AIC = 89.2 dan MSE=15.989.

Keywords

Collaboration network of the authors

22 authors · 44 co-authorship links · 4 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Jenderal Soedirman University
  • Shizuoka University
  • Universitas Halu Oleo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Rifai NurAffiliation unknown2
Muhammad Rifki NisardiAffiliation unknown2
Suroso SurosoJenderal Soedirman University1
Daru Tri NugrohoJenderal Soedirman University1
Toshihiko NoguchiShizuoka University1
La Ode SafiuddinAffiliation unknown1
I Nyoman SudianaAffiliation unknown1
Jamiludin JamiludinUniversitas Halu Oleo1
Jamiludin amiludinAffiliation unknown1
kusnaeni kusnaeniAffiliation unknown1
Nur RahmiAffiliation unknown1
Muhammad Arkam ArifuddinAffiliation unknown1
Georgina M. TinungkiAffiliation unknown1
Hanifah LainunAffiliation unknown1
Muh. Idil IslamiAffiliation unknown1
A. Kresna JayaAffiliation unknown1
Bambang BakriAffiliation unknown1
Wahyuni EkasasmitaAffiliation unknown1
Restu Ananda PutraAffiliation unknown1
Sri Muslihah BakhtiarAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Forecasting Time Series Data Using Haar Discrete Wavelet Transformation</dc:title>
	<dc:title xml:lang="id">PERAMALAN DATA DERET WAKTU MENGGUNAKAN TRANSFORMASI WAVELET DISKRIT HAAR</dc:title>
	<dc:creator xml:lang="en">Husain, Hartina</dc:creator>
	<dc:creator xml:lang="en">Amran, Amran</dc:creator>
	<dc:subject xml:lang="en">Discrete Wavelet Transform</dc:subject>
	<dc:subject xml:lang="en">Fourier Transform</dc:subject>
	<dc:subject xml:lang="en">Haar Wavelet</dc:subject>
	<dc:subject xml:lang="en">Periodogram</dc:subject>
	<dc:subject xml:lang="en">Fisher's Test</dc:subject>
	<dc:description xml:lang="en">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.</dc:description>
	<dc:description xml:lang="id">Transformasi Wavelet Diskrit merupakan metode transformasi data yang merepresentasikan data dalam domain waktu dan domain frekuensi. Transformasi ini muncul untuk mengatasi kelemahan transformasi Fourier yang hanya mampu memberikan satu informasi domain saja dan terbatas pada windowing tertentu. Jenis wavelet yang digunakan yaitu Wavelet Haar. Identifikasi keperiodikan data menggunakan analisis Periodogram dengan statistik Uji Fisher. Data hasil transformasi didekomposisi menjadi dua komponen yaitu koefisien Aproksimasi dan Koefisien Detail. Kedua komponen tersebut diramalkan menggunakan metode ARIMA Box-Jenkins. Pemilihan model dilakukan menggunakan metode Akaike Information Criterion (AIC) dan Mean Square Error (MSE). Peramalan yang diperoleh kemudian dikonstruksi kembali ke domain waktu (invers). Aplikasi model ARIMA melalui transformasi wavelet pada data Kelembaban Udara Kota Makassar periode September 2006 - Desember 2012 menunjukkan bahwa peramalan pada Koefisien Aproksimasi diperoleh model ARIMA (0,0,3) dengan nilai AIC = 112.2142 dan MSE=29.673 . Sementara peramalan pada Koefisien Detail diperoleh model ARIMA (2,1,0) dengan AIC = 89.2 dan MSE=15.989.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-05-05</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/24807</dc:identifier>
	<dc:identifier>10.20956/j.v19i3.24807</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 3 (2023): MAY, 2023; 484-497</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/24807/9710</dc:relation>
	<dc:relation>10.20956/j.v19i3.24807.g9710</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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