Sains Malaysiana 51(3)(2022): 895-909

http://doi.org/10.17576/jsm-2022-5103-23

Optimal Adaptive Neuro-Fuzzy Inference System Architecture for Time Series Forecasting with Calendar Effect

(Seni Bina Sistem Inferens Neuro-Kabur Adaptif Optimum untuk Ramalan Siri Masa dengan Kesan Kalendar)

PUTRIAJI HENDIKAWATI^1,2,*, SUBANAR¹, ABDURAKHMAN¹ & TARNO³

¹Department of Mathematics, Gadjah Mada University, Yogyakarta, Indonesia

  ²Department of Mathematics, Universitas Negeri Semarang, Semarang, Indonesia

  ³Department of Statistics, Universitas Diponegoro, Semarang, Indonesia

Received: 19 January 2021/Accepted: 13 August 2021

Abstract

This paper discusses a procedure for model selection in ANFIS for time series forecasting with a calendar effect. Calendar effect is different from the usual trend and seasonal effects. Therefore, when it occurs, it will affect economic activity during that period and create new patterns that will result in inaccurate forecasts for decision making if not considered. The focus is on the model selection strategy to find the appropriate input variable and the number of membership functions (MFs) based on the Lagrange Multiplier (LM) test. The ARIMAX stochastic model is used at the preprocessing stage to capture calendar variations in the data. The calendar effect observed is the Eid al-Fitr holiday in Indonesia, a country with the largest Muslim population in the world. The data of Tanjung Priok port passengers used as a case study. The result shows that hybrid ARIMAX-ANFIS based on the LM test can be an effective procedure for model selection in ANFIS for time series with calendar effect forecasting. Empirical results show that the use of the calendar effect variable provides more accurate predictions as indicated by smaller RMSE and MAPE values than without the calendar effect variable.

Keywords: ANFIS; ARIMAX; calendar effect; LM test; time series

Abstrak

Kertas ini membincangkan prosedur pemilihan model ANFIS untuk peramalan siri masa dengan kesan kalendar. Kesan kalendar berbeza daripada aliran biasa dan kesan bermusim. Oleh itu, apabila ia berlaku, ia akan menjejaskan aktiviti ekonomi dalam tempoh tersebut dan mewujudkan corak baharu yang akan mengakibatkan ramalan yang tidak tepat untuk membuat keputusan jika tidak dipertimbangkan. Fokus adalah pada strategi pemilihan model untuk mencari pemboleh ubah input yang sesuai dan bilangan fungsi keahlian (MF) berdasarkan ujian Pengganda Lagrange (LM). Model stokastik ARIMAX digunakan pada peringkat prapemprosesan untuk mengesan variasi kalendar dalam data. Kesan kalendar yang diperhatikan ialah cuti Hari Raya Aidilfitri di Indonesia, sebuah negara dengan penduduk Islam terbesar di dunia. Data penumpang pelabuhan Tanjung Priok digunakan sebagai kajian kes. Keputusan menunjukkan bahawa ARIMAX-ANFIS hibrid berdasarkan ujian LM boleh menjadi prosedur yang berkesan untuk pemilihan model dalam ANFIS dalam siri masa dengan ramalan kesan kalendar. Keputusan empirik menunjukkan bahawa penggunaan pemboleh ubah kesan kalendar memberikan ramalan yang lebih tepat seperti yang ditunjukkan oleh nilai RMSE dan MAPE yang lebih kecil berbanding tanpa pemboleh ubah kesan kalendar.

Kata kunci: ANFIS; ARIMAX; kesan kalendar; siri masa; ujian LM

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^*Corresponding author; email: putriaji.mat@mail.unnes.ac.id