### PERAMALAN JUMLAH PENUMPANG KERETA API MENGGUNAKAN METODE ARIMA, INTERVENSI DAN ARFIMA (Studi Kasus : Penumpang Kereta Api Kelas Lokal EkonomiDAOP IV Semarang)

*Helmi Panjaitan  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia
Alan Prahutama  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia
Sudarno Sudarno  -  Departemen Statistika, Fakultas Sains dan Matematika, Universitas Diponegoro, Indonesia
Published: 28 Feb 2018.

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Abstract

Autoregressive Integrated Moving Average (ARIMA) is stationary time series model after differentiation. Differentiation value of ARIMA method is an integer so it is only able to model in the short term. The best model using ARIMA method is ARIMA([13]; 1; 0) with an MSE value of 1,870844. The Intervention method is a model for time series data which in practice has extreme fluctuations both up and down. In the data plot the number of train passengers was found to be extreme fluctuation. The data used was from January 2009 to June 2017 where fluctuation up significantly in January 2016 (T=85 to T=102) so the intervention model that was suspected was a step function. The best model uses the Intervention step function is ARIMA ([13]; 1; 1) (b=0; s=18; r=0) with MSE of 1124. Autoregressive Fractionally Integrated Moving Average (ARFIMA) method is a development of the ARIMA method. The advantage of the ARFIMA method is the non-integer differentiation value so that it can overcome long memory effect that can not be solve with the ARIMA method. ARFIMA model is capable of modeling high changes in the long term (long term persistence) and explain long-term and short-term correlation structures at the same time. The number of local economy class train passengers in DAOP IV Semarang contains long memory effects, so the ARFIMA method is used to obtain the best model. The best model obtained is the ARMA(0; [1,13]) model with the differential value is 0,367546, then the model can be written into ARFIMA (0; d; [1,13]) with an MSE value of 0,00964. Based on the analysis of the three methods, the best method of analyzing the number of local economy class train passengers in DAOP IV Semarang is the ARFIMA method with the model is ARFIMA (0; 0,367546; [1,13]).

Keywords: Train Passengers, ARIMA, Intervention, ARFIMA, Forecasting

Keywords: Train Passengers, ARIMA, Intervention, ARFIMA, Forecasting

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