An Application of Permutation Entropy and Multiscale Complexity in the Gold Market

Rini Mayasari; Nono Heryana

doi:10.35377/saucis...1955708

An Application of Permutation Entropy and Multiscale Complexity in the Gold Market

Abstract

This study compares the ordinal complexity of daily gold futures log returns rt , overlapping 20-day rolling variance RV20, and log-prices lnPt using permutation entropy (PE) and multiscale permutation entropy (MPE). The sample comprises 4,104 unadjusted closing prices for gold futures (GC=F) from Yahoo Finance, covering 4 January 2010 to 30 April 2026. Full-sample normalized return PE is 0.9963 at embedding order m = 5, close to the theoretical maximum and compatible with weak-form informational efficiency at the daily frequency. High PE describes ordinal randomness, not the absence of forecastability or profitable trading opportunities. At m = 5, PE is lower for log-prices (0.9219) and RV20 (0.9082), indicating stronger ordinal structure. Returns contain all 120 possible patterns for m = 5, and the chi-squared test does not reject uniformity (χ2 = 142.1, d f = 119, p = 0.073). Across scales τ = 1, . . . ,10, the Complexity Index (CI) is 9.826 for returns, 8.695 for RV20, and 8.476 for log-prices. The return CI lies within its 95% reference interval from seeded i.i.d. surrogates; the RV20 and log-price CIs fall below their corresponding intervals. The lowest scale-5 return PE occurs in 2018–2021 (0.9711), but remains within its 95% i.i.d.-surrogate interval and does not establish a statistically distinct crisis regime. The comparison distinguishes near-random daily return orderings from multiscale structure in volatility-related and price-level transformations.

Keywords

Ethical Statement

This study did not involve human participants, animals, or identifiable personal data. The authors confirm that the research was conducted in accordance with applicable scientific and ethical standards.

Thanks

The authors gratefully acknowledge Universitas Singaperbangsa Karawang, Indonesia, for its institutional and academic support in facilitating this research.

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Details

Primary Language

English

Subjects

Spatial Data and Computing Applications, Applied Computing (Other), Artificial Intelligence (Other)

Journal Section

Research Article

Authors

Rini Mayasari ^*
0009-0003-3431-1528
Indonesia

Nono Heryana
0000-0003-4969-9353
Indonesia

Early Pub Date

October 27, 2026

Publication Date

October 30, 2026

Submission Date

May 20, 2026

Acceptance Date

September 7, 2026

Published in Issue

Year 2026 Volume: 9 Number: 5

DOI

https://doi.org/10.35377/saucis...1955708

IZ

https://izlik.org/JA65TP99SD

Cite

RIS / Bibtex

APA

Mayasari, R., & Heryana, N. (2026). An Application of Permutation Entropy and Multiscale Complexity in the Gold Market. Sakarya University Journal of Computer and Information Sciences, 9(5), 1504-1511. https://doi.org/10.35377/saucis...1955708

AMA

1.Mayasari R, Heryana N. An Application of Permutation Entropy and Multiscale Complexity in the Gold Market. SAUCIS. 2026;9(5):1504-1511. doi:10.35377/saucis.1955708

Chicago

Mayasari, Rini, and Nono Heryana. 2026. “An Application of Permutation Entropy and Multiscale Complexity in the Gold Market”. Sakarya University Journal of Computer and Information Sciences 9 (5): 1504-11. https://doi.org/10.35377/saucis. 1955708.

EndNote

Mayasari R, Heryana N (October 1, 2026) An Application of Permutation Entropy and Multiscale Complexity in the Gold Market. Sakarya University Journal of Computer and Information Sciences 9 5 1504–1511.

IEEE

[1]R. Mayasari and N. Heryana, “An Application of Permutation Entropy and Multiscale Complexity in the Gold Market”, SAUCIS, vol. 9, no. 5, pp. 1504–1511, Oct. 2026, doi: 10.35377/saucis...1955708.

ISNAD

Mayasari, Rini - Heryana, Nono. “An Application of Permutation Entropy and Multiscale Complexity in the Gold Market”. Sakarya University Journal of Computer and Information Sciences 9/5 (October 1, 2026): 1504-1511. https://doi.org/10.35377/saucis. 1955708.

JAMA

1.Mayasari R, Heryana N. An Application of Permutation Entropy and Multiscale Complexity in the Gold Market. SAUCIS. 2026;9:1504–1511.

MLA

Mayasari, Rini, and Nono Heryana. “An Application of Permutation Entropy and Multiscale Complexity in the Gold Market”. Sakarya University Journal of Computer and Information Sciences, vol. 9, no. 5, Oct. 2026, pp. 1504-11, doi:10.35377/saucis. 1955708.

Vancouver

1.Rini Mayasari, Nono Heryana. An Application of Permutation Entropy and Multiscale Complexity in the Gold Market. SAUCIS. 2026 Oct. 1;9(5):1504-11. doi:10.35377/saucis. 1955708