A Reliability-Based Survival Analysis Framework for Gold Price Risk Assessment: A Methodological Demonstration

Abstract

Gold is widely regarded as a safe-haven asset and occupies a prominent position in investment portfolios during periods of economic uncertainty. Previous research has concentrated overwhelmingly on forecasting gold prices using econometric and machine-learning techniques, whereas the assessment of gold price risk from the perspective of reliability theory has received little attention. This study demonstrates how reliability and survival analysis methods may be applied to the timing of adverse gold price events. The data are daily settlement prices of COMEX gold futures in US dollars per troy ounce for 1 January 2014 to 6 January 2025 (2,565 trading days). A failure event is defined as a price falling below the twentieth percentile of the observed full-sample distribution, and the interval between consecutive failures is treated as the time-to-failure variable.

The Kaplan–Meier estimator is used to obtain a non-parametric estimate of the reliability function, and the cumulative hazard function, obtained as the negative logarithm of the reliability estimate, is used to describe the accumulation of failure risk. Weibull and Exponential parametric lifetime models are fitted by maximum likelihood, compared by likelihood ratio test and by the Akaike and Bayesian information criteria, and used to estimate the Mean Time to Failure (MTTF).

Under the stated failure definition, 513 of 2,565 daily observations (20.00%) were classified as failures and the Kaplan–Meier reliability estimate was 0.8000 (95% CI 0.7847–0.8156), with a terminal cumulative hazard of 0.223. The Weibull model fitted substantially better than the Exponential (likelihood ratio statistic 350.55 on 1 degree of freedom, p < 0.001; AIC 9904.98 versus 10253.53), with an estimated shape parameter of 2.38 and a scale parameter of 3289. The corresponding MTTF estimates were 2,918 and 8,065 trading days respectively, both of which exceed the 2,565-day observation window and therefore rest on extrapolation beyond the range of the data.

These results are reported alongside an explicit assessment of what they can and cannot support. Because the failure threshold is a fixed percentile of the same distribution from which failures are counted, the failure proportion, the terminal reliability estimate and the terminal cumulative hazard are determined by the threshold rather than estimated from the data; they are reported here for completeness rather than as substantive findings about gold. Further, the parametric models were fitted on the trading-day index rather than on inter-failure times, and the fitted Weibull implies a cumulative failure probability of 42.5% by day 2,565 against a Kaplan–Meier estimate of 20.0%, so neither parametric model reproduces the non-parametric curve. The contribution of this paper is therefore methodological: it sets out how reliability concepts map onto commodity price risk, identifies precisely where the mapping breaks down when applied to a trending, autocorrelated price level, and specifies the redesign required for the framework to yield interpretable risk estimates.