DOI: 10.35377/saucis...1955708 ISSN: 2636-8129

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

Rini Mayasari, Nono Heryana
Show PDF Cite
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.

More from our Archive