Comparative Analysis of Mathematical Models: A Case Study of Used Smartphone Price Depreciation
DOI:
https://doi.org/10.12962/limits.v22i2.3469Keywords:
Depriciation, Exponential decay, Holt-winters damped, Logistic decay, Prediction, SmartphoneAbstract
The price depression of the smartphone after it becomes used is one of the factors that consumers should consider when buying used smartphones. Therefore, accurate prediction of the price of used smartphones becomes a better insight into marketing strategies, and consumer purchasing decisions. The study aims to compare the performance of the Holt-Winters model damped, logistical decay, and exponential decay to predict the price depression of used smartphones. This research method uses historical data from some used smartphone prices as a basis for analysis. Comparisons between the three models were made to assess the performance of each in representing price depression behavior. Then, a statistical analysis was conducted to determine the most optimal model in predicting the price depression of used smartphones, the optimity of a model measured by the accuracy and speed of the computer performing the model execution. The accuracy measure in this study is the mean square error (MSE) value generated by a model with historical data alignment based on the ratio to the price when the smartphone has not been indicated as usable and the execution speed measure is the time it takes a computer to execute the model. The results show that the Holt-Winters damped model provides the most optimal predictive results compared to the exponential and decay models. This is demonstrated by the lower MSE average value twice as low as compared with the other two models, on the other hand, the holt-winters Damped has the weakness of requiring the longest average execution time of the three models with an average performance speed of 2.7 seconds, but the shortfall is not fatal because the predicted time period in this case is monthly so there is no urgency to advance the speed of seconds rather than accuracy.
Downloads
References
M. Rahmatillah and M. Tharziansyah, "Pusat Barang Bekas Layak Pakai Di Kota Banjarbaru.," JURNAL TUGAS AKHIR MAHASISWA LANTING, vol. 11, no. 1, pp. 189-199, 2022.
A. Aksenta, I. Irmawati, A. Ridwan, N. Hayati, S. Sepriano, H. Herlinah, A. Silalah, S. Pipin, I. Abdurrohim, Y. Boari and S. Mardiana, LITERASI DIGITAL: Pengetahuan & Transformasi Terkini Teknologi Digital Era Industri 4.0 dan Sociaty 5.0, Jambi: PT. Sonpedia Publishing Indonesia, 2023.
I. Kiki, "ANALISIS PENGARUH HARGA, PRODUK, TEMPAT DAN PROMOSI TERHADAP KEPUTUSAN PEMBELIAN HANDPHONE BEKAS (Studi Pada Konsumen Handphone Bekas Daerah Kabupaten Cilacap dan Sekitarnya).," UIN Prof. KH Saifuddin Zuhri, Purwokerto, 2023.
V. S. Maharani, S. Hartono and S. Maryam, " Pengaruh Gaya Hidup, Brand Image, dan Persepsi Harga terhadap Keputusan Pembelian iPhone Secondhand Internasional di Surakarta," In Social, Humanities, and Educational Studies (SHES): Conference Series )., vol. 8, no. 2, 2025.
Noviani, N.M., Yuliastuti, I. A. N. and L. K. Merawati, "Pengaruh Profitabilitas, Likuiditas, Leverage, Manajemen Aset, Dan Inflasi Terhadap Nilai Perusahaan Di BEI.," KARMA (Karya Riset Mahasiswa Akuntansi), vol. 2, no. 1, pp. 2232-2240, 2022.
J. Julianto, "Pengaruh Perputaran Total Aset, Pertumbuhan Aset, dan Kebijakan Utang terhadap Nilai Perusahaan Sektor Barang Konsumen Primer di Bursa Efek Indonesia.," FIN-ACC (Finance Accounting), vol. 8, no. 2, pp. 200-210, 2022.
J. Jihad, "PENGARUH HARGA, KUALITAS PRODUK, DAN CITRA MEREK TERHADAP MINAT BELI SMARTPHONE BEKAS DI KOTA PALOPO.," Institut Agama Islam Negeri Palopo, Palopo, 2023.
Y. Putri, R. Sulbahri and G. Kusuma, "Pengaruh Strategi Green Marketing Terhadap Kinerja Keuangan Dan Non-Keuangan Perusahaan.," Akuntansi Dan Manajemen, vol. 18, no. 1, pp. 33-50, 2023.
B. Harto, A. Rukmana, Y. Boari, M. Rusliyadi, D. Aldo, P. Juliawati and Y. Dewi, WIRAUSAHA BIDANG TEKNOLOGI INFORMASI: Peluang usaha dalam meyongsong era society 5.0, Jambi: PT. Sonpedia Publishing Indonesia, 2023.
M. Sahinli, "Potato price forecasting with Holt-Winters and ARIMA methods: A case study.," American Journal of Potato Research, vol. 97, no. 4, pp. 336-346, 2020.
R. Bhardwaj, "A predictive model for the evolution of COVID-19.," Transactions of the Indian National Academy of Engineering, vol. 5, no. 1, pp. 133-140, 2020.
C. Liu, Y. Shan, W. Sun, C. Yan and K. Yang, "An open channel with an emergent vegetation patch: Predicting the longitudinal profiles of velocities based on exponential decay.," Journal of Hydrology, no. 582, p. 124429, 2020.
H. Janis and Y. Samalukang, "Analisis dan pemodelan perubahan temporal dan variasi spasial suhu air laut di Gunung Api Bawah Laut Mahengetang.," Jurnal Ilmu Kelautan Kepulauan, vol. 3, no. 2, 2020.
K. Wu, D. Darcet, Q. Wang and D. Sornette, "Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world.," Nonlinear dynamics , vol. 101, no. 3, pp. 1561-1581, 2020.
R. Rushton, O. Lorraine, J. Tiong, M. Karim, R. Dixon, W. Greenshields, R. Marotti and N. Bretana, "Forecasting inventory for the state-wide pharmaceutical service of South Australia.," Procedia Computer Science, no. 219, pp. 1257-1264, January 2023.
C. Vaghi, A. Rodallec, R. Fanciullino, J. Ciccolini, J. Mochel, M. Mastri, C. Poignard, J. Ebos and S. Benzekry, "Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors.," PLoS computational biology, vol. 16, no. 2, p. e1007178, 2020.
D. Montoya, B. Haegeman, S. Gaba, C. D. Mazancourt and M. Loreau, "Habitat fragmentation and food security in crop pollination systems.," Journal of Ecology, vol. 109, no. 8, pp. 2991-3006, 2021.
M. Mursidah, Y. Yunina, N. Nurhasanah and D. Yuni, "Perbandingan Metode Exponential Smoothing dan Metode Decomposition Untuk Meramalkan Persediaan Beras (Studi Kasus Divre Bulog Lhokseumawe).," Jurnal Visioner & Strategis, vol. 10, no. 1, 2021.
D. Hartono, "Prototipe Sistem Monitoring Daya Listrik Berbasis Internet of Things (IoT) Menggunakan Metode Exponential Smoothing Untuk Prediksi Kebutuhan Energi.," Universitas Islam Sultan Agung, Semarang, 2023.
D. Kartika, D. Novitasari and F. Setiawan, "Prediksi Kecepatan Arus Laut Di Perairan Selat Bali Menggunakan Metode Exponential Smoothing Holt-Winters.," MathVision: Jurnal Matematika, vol. 2, no. 1, pp. 12-17, 2020.
M. Vikri and R. Rohmah, "Penerapan Fungsi Exponential Pada Pembobotan Fungsi Jarak Euclidean Algoritma K-Nearest Neighbor.," Generation Journal, vol. 6, no. 2, pp. 98-105, 2022.
I. Sari and A. Utami, Rekayasa Perangkat Lunak Berorientasi Objek Menggunakan PHP, Yogyakarta: Penerbit Andi, 2021.
R. Sukmono, "Buku Ajar Supply Chain Management Theory and Practice.," Umsida Press, pp. 1-73, 2021.
R. Aviyolla, A. Santoso and D. Praditya, "Analisis dan Perancangan Arsitektur Perusahaan Menggunakan Kerangka Kerja TOGAF ADM 9.2 pada Fungsi IT Support PT. XYZ.," eProceedings of Engineering, vol. 10, no. 6, 2023.
T. Nababan, B. Warsito and A. Rusgiyono, "Pemodelan Wavelet Neural Network untuk Prediksi Nilai Tukar Rupiah Terhadap Dolar AS.," Jurnal Gaussian, vol. 9, no. 2, pp. 217-226, 2020.
I. Id, Machine Learning: Teori, Studi Kasus dan Implementasi Menggunakan Python, Pekanbaru: Unri Press, 2021.
S. Stanley, A. Banda, B. Kasense, I. Siluyele and E. Moyo, "Forecasting annual international tourist arrivals in Zambia using Holt-Winters exponential smoothing.," Open Journal of Statistics, vol. 9, no. 2, pp. 258-267, 2019.
S. Oliver, "Annual Phone Depreciation Report - musicMagpie," musicMagpie, [Online]. Available: https://www.musicmagpie.co.uk/phone-depreciation/. [Accessed 11 January 2024].
R. Anandanatarajan, U. Mangalanathan and U. Gandhi, "Linearization of temperature sensors (K-type thermocouple) using polynomial non-linear regression technique and an IoT-based data logger interface.," Experimental Techniques, vol. 47, no. 4, pp. 885-894, 2023.
C. Shen, "Logistic growth modelling of COVID-19 proliferation in China and its international implications.," International Journal of Infectious Diseases, no. 96, pp. 582-589, 2020.
M. Kommenda, B. Burlacu, G. Kronberger and M. Affenzeller, "Parameter identification for symbolic regression using nonlinear least squares.," Genetic Programming and Evolvable Machines, vol. 21, no. 3, pp. 471-501, 2020.
S. Xu, Q. Zhou and W. Liu, "Prediction of soliton evolution and equation parameters for NLS–MB equation based on the phPINN algorithm.," Nonlinear Dynamics, vol. 111, no. 19, pp. 18401-18417, 2023.
L. Fodor, D. Jakovetic, N. Krejic and G. Malaspina, "Parallel Inexact Levenberg-Marquardt Method for Nearly-Separable Nonlinear Least Squares.," arXiv preprint arXi, vol. 2312.09064, 2023.
Z. Han, X. Zhang, B. Yan, L. Qiao and Z. Li, "Methods on the determination of the circuit parameters in an underwater spark discharge.," Mathematical Problems in Engineering, no. 1, p. 7168375, 2022.
D. Wibowo, D. Adytia and D. Saepudin, "Prediction of tide level by using holtz-winters exponential smoothing: Case study in cilacap bay.," International Conference on Data Science and Its Applications (ICoDSA), pp. 1-5, 2020.
H. d. l. Fuente-Mella, C. Elórtegui-Gómez, B. Umaña-Hermosilla, M. Fonseca-Fuentes and G. Ríos-Vásquez, "Stochastic Approaches Systems to Predictive and Modeling Chilean Wildfires.," Mathematics, vol. 11, no. 20, p. 4346, 2023.
C. Syavasya and A. L. Muddana, "Machine learning based time series prediction using holt-winters exponential smoothing with multiplicative seasonality.," 5th International Conference on Electrical, Electronics, Communication, Computer Technologies and Optimization Techniques (ICEECCOT), pp. 174-182, 2021.
O. Trull, J. García-Díaz and A. Troncoso, "Initialization methods for multiple seasonal Holt–Winters forecasting models.," Mathematics, vol. 8, no. 2, p. 268, 2020.
K. Wu, D. Darcet, Q. Wang and D. Sornette, "Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world.," Nonlinear dynamics, vol. 101, no. 3, pp. 1561-1581, 2020.
E. Postnikov, "Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?.," Chaos, Solitons & Fractals, no. 135, p. 109841, 2020.
J. Gao, H. Wang and H. Shen, "Task failure prediction in cloud data centers using deep learning.," IEEE transactions on services computing, vol. 15, no. 3, pp. 1411-1422, 2020.
J. Bauer and D. Groneberg, "Measuring spatial accessibility of health care providers–introduction of a variable distance decay function within the floating catchment area (FCA) method.," PloS one, vol. 11, no. 7, p. e0159148, 2016.
H. Sinaga and N. Irawati, "A medical disposable supply demand forecasting by moving average and exponential smoothing method.," Proceedings of the 2nd Workshop on Multidisciplinary and Applications (WMA), 2018.
J. Hogg, M. Fonoberova and I. Mezic, "Exponentially decaying modes and long-term prediction of sea ice concentration using Koopman mode decomposition," Scientific reports, vol. 10, no. 1, p. 16313, 2020.
S. Tuda and S. Rexhepi, "Exploring Exponential Functions Using Geogebra.," Brillo Journal, vol. 3, no. 1, pp. 43-58, 2023.
L. Amalia, W. Ramdhan and W. Kifti, "Penerapan Metode Trend Moment Untuk Memprediksi Jumlah Pertumbuhan Penduduk.," Building of Informatics, Technology and Science (BITS), vol. 3, no. 4, pp. 566-573, 2022.
M. Rini and N. Ananda, "Perbandingan Metode Peramalan Menggunakan Model Time Series.," Tekinfo: Jurnal Ilmiah Teknik Industri dan Informasi, vol. 10, no. 2, pp. 88-101, 2022.
A. Siregar, "Klasifikasi Untuk Prediksi Cuaca Menggunakan Esemble Learning.," Petir, vol. 13, no. 2, 2020.
I. Pradnyana, P. Arya and I. Sunaya, "Peramalan Hasil Studi Terhadap Kehadiran Mahasiswa Menggunakan Metode Backpropagation.," Jurnal Inovasi Teknologi dan Edukasi Teknik, vol. 2, no. 1, pp. 20-26, 2022.
B. Atmaja and M. Akagi, "Evaluation of error-and correlation-based loss functions for multitask learning dimensional speech emotion recognition.," Journal of Physics: Conference Series, vol. 1896, no. 1, p. 012004, 2021.
X. Dai and A. Burns, "Period adaptation of real-time control tasks with fixed-priority scheduling in cyber-physical systems.," Journal of systems architecture, no. 103, p. 101691, 2020.
