Penerapan Modified Jackknife Kibria-Lukman Regression dengan Koreksi Autokorelasi Prais-Winsten pada Nilai Tukar Rupiah terhadap Dolar Amerika Serikat

Chrisadna Patricia Kabangnga, A. Muthiah Nur Angriany, Raupong Raupong

Abstract


The movement of the Indonesian Rupiah exchange rate against the United States Dollar (USD) experienced volatility during the 2021-2024 period, thus requiring precise analysis to identify the factors influencing it. This modeling can be conducted through multiple linear regression analysis; however, parameter estimation using Ordinary Least Squares (OLS) is often inefficient and prone to producing large variances due to the violation of assumptions in the form of multicollinearity and autocorrelation. Therefore, this study aims to model the Rupiah exchange rate against the USD for the 2021–2024 period and identify the significantly influencing factors using the Modified Jackknife Kibria-Lukman Regression (MJKLR) method with Prais-Winsten (PW) autocorrelation correction. Autocorrelation handling was performed through the PW correction, followed by MJKLR modeling on the PW-transformed data to reduce the impact of multicollinearity. The results showed that the MJKLR-PW estimator provided a more efficient performance compared to OLS-PW and KLR-PW, with an estimator MSE of 0.1877, RMSE of 326.1730, and an adjusted R² value of 72.54%. The variables of money supply, interest rate, total exports, and total imports had a significant effect on the Rupiah exchange rate at a 5% significance level. In conclusion, the combination of MJKLR and PW is effective in modeling the Rupiah exchange rate against the USD that has autocorrelation and multicollinearity problems. Empirically, this study indicates that the stability of the Rupiah exchange rate relies heavily on macroeconomic fundamentals, particularly monetary policy and the trade balance.

Keywords


Autocorrelation; Modified Jackknife Kibria-Lukman Regression; Multicollinearity; Rupiah Exchange Rate Against the United States Dollar; Prais-Winsten

Full Text:

PDF

References


G. Mardiatmoko, “Pentingnya uji asumsi klasik pada analisis regresi linier berganda (studi kasus penyusunan persamaan allometrik kenari muda [Canarium indicum L.]),” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 14, no. 3, pp. 333–342, Sep. 2020, doi:10.30598/barekengvol14iss3pp333-342.

N. U. Martaningtyas, E. A. Septiyaningrum, and Z. Maulana, “Dampak pelanggaran asumsi klasik terhadap kesalahan inferensi dalam analisis ekonometrika,” Synergy: Jurnal Ilmiah Multidisiplin, vol. 1, no. 04, pp. 255–265, Dec. 2023.

D. N. Gujarati and D. C. Porter, Basic Econometrics, 5th ed. New York: McGraw-Hill/Irwin, 2009.

W. H. Greene, Econometric Analysis, 7th ed. New York: Pearson Education, 2012.

A. D. A. S. Budi, L. Septiana, and B. E. P. Mahendra, “Memahami asumsi klasik dalam analisis statistik: Sebuah kajian mendalam tentang multikolinearitas, heterokedastisitas, dan autokorelasi dalam penelitian,” Jurnal Multidisiplin West Science, vol. 03, no. 01, pp. 1–11, 2024, doi:10.58812/jmws.v3i01.878.

J. M. Wooldridge, Introductory Econometrics: A Modern Approach, 5th ed. Mason, Ohio: South-Western Cengage Learning, 2013.

B. M. G. Kibria and A. F. Lukman, “A new ridge-type estimator for the linear regression model: Simulations and applications,” Scientifica, vol. 2020, no. 1, p. 9758378, 2020, doi:10.1155/2020/9758378.

F. I. Ugwuowo, H. E. Oranye, and K. C. Arum, “On the jackknife Kibria-Lukman estimator for the linear regression model,” Communications in Statistics - Simulation and Computation, vol. 52, no. 12, pp. 6116–6128, 2023, doi:10.1080/03610918.2021.2007401.

R. E. Park and B. M. Mitchell, “Estimating the autocorrelated error model with trended data,” Journal of Econometrics, vol. 13, no. 2, pp. 185–201, 1980, doi:10.1016/0304-4076(80)90014-7.

A. I. Parapa, “Pemodelan ridge regression pada data time series dengan koreksi autokorelasi Prais-Winsten (studi kasus: Nilai tukar Rupiah terhadap Dolar Amerika Serikat),” Skripsi, Universitas Hasanuddin, Makassar, 2025, Fakultas Matematika dan Ilmu Pengetahuan Alam, Program Studi Statistika.

M. A. Zubair and M. O. Adenomon, “Comparison of estimators efficiency for linear regressions with joint presence of autocorrelation and multicollinearity,” Science World Journal, vol. 16, no. 2, pp. 103–109, 2021.

A. Putri, R. Santoso, and S. Sugito, “Analisis regresi nonparametrik kernel menggunakan metode jackknife sampel terhapus-1 dan sampel terhapus-2 (studi kasus: Pemodelan tingkat inflasi terhadap nilai tukar Rupiah di Indonesia periode 2004–2016),” Jurnal Gaussian, vol. 6, no. 1, pp. 1–10, 2017.

R. Cahyadi, R. A. Yunanda, R. S. Putra, S. I. Jaya, S. P. Bayu, and N. Rizki, “Analisis faktor-faktor melemahnya kurs Rupiah pada era digital,” Jurnal Ilmu Ekonomi Manajemen dan Akuntansi MH Thamrin, vol. 5, no. 2, pp. 412–427, 2024, doi:10.37012/ileka.v5i2.2341.

D. Permatasari, “Analisis pengaruh suku bunga, jumlah uang beredar, inflasi, neraca transaksi berjalan, cadangan devisa, indeks produksi terhadap kurs valuta asing periode 2010–2024,” Skripsi, Universitas Islam Indonesia, Yogyakarta, 2025.

Y. R. Hakim and T. S. Aji, “Factors affecting the exchange rate of the Indonesian Rupiah against the United States Dollar: January 2013–December 2023,” Formosa Journal of Multidisciplinary Research, vol. 4, no. 5, pp. 2043–2062, 2025, doi:10.55927/fjmr.v4i5.175.

A. Prahutama and R. Rahmawati, “Analisis regresi linier berganda pada data survei untuk pemodelan total pengeluaran di Jawa Tengah, Indonesia,” Jurnal Gaussian, vol. 13, no. 2, pp. 394–404, 2024, doi:10.14710/j.gauss.13.2.394-404.

D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to Linear Regression Analysis, 5th ed. Hoboken, New Jersey: John Wiley & Sons, Inc., 2012.

P. Mishra, C. M. Pandey, U. Singh, A. Gupta, C. Sahu, and A. Keshri, “Descriptive statistics and normality tests for statistical data,” Annals of Cardiac Anaesthesia, vol. 22, no. 1, pp. 67–72, 2019, doi:10.4103/aca.ACA_157_18.

S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality (complete samples),” Biometrika, vol. 52, no. 3–4, pp. 591–611, 1965, doi:10.1093/biomet/52.3-4.591.

W. W. S. Wei, Time Series Analysis: Univariate and Multivariate Methods, 2nd ed. New York: Pearson Education, 2006.

C. Bottomley, M. Ooko, A. Gasparrini, and R. Keogh, “In praise of Prais-Winsten: An evaluation of methods used to account for autocorrelation in interrupted time series,” Statistics in Medicine, vol. 42, no. 8, pp. 1277–1288, 2023, doi:10.1002/sim.9669.

W. F. Syafni, “Kibria-Lukman estimator untuk menangani multikolinearitas dalam analisis regresi logistik pada dataset audio akord mayor dan minor,” Skripsi, Universitas Gadjah Mada, Yogyakarta, 2024, Fakultas Matematika dan Ilmu Pengetahuan Alam, Program Studi Statistika.

H. E. Oranye et al., “Selection of a new biasing parameter for the jackknife Kibria-Lukman estimator for the negative binomial regression model,” NIPES-Journal of Science and Technology Research, vol. 7, no. 1, pp. 257–266, 2025, doi:10.37933/nipes/7.1.2025.SI30.

A. E. Hoerl and R. W. Kennard, “Ridge regression by automated selection of k,” Technometrics, vol. 19, no. 1, pp. 35–40, 1977, doi:10.1080/00401706.1977.10489550.

E. Ä. Duran and F. Akdeniz, “Efficiency of the modified jackknifed Liu-type estimator,” Statistical Papers, vol. 53, no. 2, pp. 265–280, 2012, doi:10.1007/s00362-010-0334-5.

G. Casella and R. L. Berger, Statistical Inference, 2nd ed. Pacific Grove, California: Brooks/Cole Thomson Learning, 2002.

A. Biriukov, S. Rasp, L. Grundner, and V. Eyring, “Root-mean-square error (RMSE) or mean absolute error (MAE): When to use them or not,” Geoscientific Model Development, vol. 15, no. 14, pp. 5481–5488, 2022, doi:10.5194/gmd-15-5481-2022.

M. H. Kutner, C. J. Nachtsheim, J. Neter, and W. Li, Applied Linear Statistical Models, 5th ed. Boston, Massachusetts: McGraw-Hill/Irwin, 2005.




DOI: https://doi.org/10.37905/euler.v14i2.38482

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Chrisadna Patricia Kabangnga, A. Muthiah Nur Angriany, Raupong Raupong

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi has been indexed by:


 EDITORIAL OFFICE OF EULER : JURNAL ILMIAH MATEMATIKA, SAINS, DAN TEKNOLOGI

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: [email protected]
 +6287777-586462 (WhatsApp Only)
 Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi (p-ISSN: 2087-9393 | e-ISSN:2776-3706) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.