Gold ARIMA's 9.15% MAPE needs a random-walk comparison

A gold trader needs to know whether ARIMA beats yesterday's close. Nyoto, Riti and Rudyanto report an ARIMA(1,1,1) win over two Monte Carlo scenarios, GBM price paths simulated at fixed volatility, across four 60-day windows. They never score it against the random walk, despite naming that benchmark in their methods and finding little autocorrelation in their own Ljung-Box test.

The forecasts and the risk layer

The authors use 1,347 daily gold futures closes from Investing.com, covering 1 March 2020 to 2 April 2026. Five models divide the work. Gold returns show kurtosis of 7.7658 and skewness of -0.7039, alongside volatility clustering. ARIMA models the mean on price levels; GARCH(1,1) models variance on log returns. For the left tail, extreme value theory uses peaks-over-threshold: it fits a generalized Pareto distribution (GPD) to returns below the empirical 5th percentile.

The geometric Brownian motion Monte Carlo generates 1,000 paths in three volatility regimes drawn from historical phases. Daily volatility is 1.02% for the 2022-23 consolidation, 1.50% for the 2024-26 geopolitical rally and 1.16% for COVID. A random walk supplies the baseline. The authors present the forecasts and risk measures as inputs to investment decisions, and say GARCH output guides position sizing. Their full-sample empirical one-day risk figures are 95% VaR of -1.8684% and CVaR of -2.9840%.

ARIMA leads the scored forecasts with 9.15% MAPE, MAE of USD 396.14 and RMSE of USD 454.31. The Monte Carlo geopolitical scenario records 10.37% MAPE; the normal scenario records 11.21%. Each of the three scored forecasters, ARIMA and both Monte Carlo scenarios, gets 100% directional accuracy. GARCH estimates alpha at 0.10 and beta at 0.85. Its April 2026 conditional volatility is 2.2817%, versus a long-run 1.2535%. For the random walk, ACF(1) is -0.016769 and Ljung-Box Q(4) is 2.9885 (p = 0.5598). The authors conclude that gold futures are weak-form efficient.

The proposed combination assigns ARIMA the price forecast, GARCH the volatility, EVT and CVaR the crisis risk, and Monte Carlo the scenarios. These are familiar tools. Riti's earlier ARIMA-versus-least-squares gold study (Anggelia, Riti and Siswanto, 2024) covered forecasting. The risk layer is the addition here, and it has to withstand scrutiny.

Where is the random-walk error?

The methods explicitly give the random walk a comparator's job: judging how well the other methods forecast gold. Yet the MAE/RMSE/MAPE table leaves it out. The authors group it with GARCH and EVT, saying those models were not designed as price point forecasters. That reason works for GARCH and EVT. The random walk supplies a point forecast directly, either the last close or the last close plus drift. We raised the same issue with USD/CAD forecasts that lost to the no-change benchmark.

The paper's diagnostics make the missing comparison especially consequential. With Ljung-Box p at 0.5598 and ACF(1) at -0.016769, the AR and MA terms have little apparent structure to fit. ARIMA(1,1,1) on differenced prices should therefore approach a random walk with drift. Its projected path has that look: from +1.41% at day 60 to +16.13% at day 360 (USD 4,762.03 to 5,453.14), it climbs in equal 30-day steps. The authors call the projection deterministic extrapolation of the differenced series' trend.

The 100% directional accuracy deserves similar caution. It covers all three scored forecasters, including two GBM scenarios driven by random normal shocks. Their four 60-day windows fall between December 2024 and April 2026, within the January 2024 to April 2026 phase. Gold rose 126.47% in that phase, with a worst drawdown of 17.97%. Positive drift would get the direction right in most such windows, and four windows give a hit rate little room to prove itself.

The evaluation design is also hard to pin down. The methods describe an 80/20 train/test split. Section 3.4 instead places the four rolling results windows in the last year of data, while section 3.9 dates them December 2024 to April 2026, about 16 months. We did not find an account of how each model was refit between windows.

The abstract crowns ARIMA the most accurate of five named models. The supporting table scores three forecasters and omits the model the abstract calls the comparator.

An infinite-mean tail

The EVT fit reports a GPD shape of 1.50 and scale of 2.88 × 10⁻⁶. At a shape of 1 or greater, mean excess loss is infinite; expected shortfall under this fit does not exist. In log-return units, the scale is effectively zero. A threshold at the 5th percentile of 1,347 returns also leaves roughly 67 exceedances for the fit.

Even so, the paper estimates a 16.21% loss at 0.1% probability, or about USD 761.27 at its USD 4,695.59 reference price. It gives expected shortfall at that level as -2.9840%, repeating the empirical 95% CVaR from section 3.3. The mean loss beyond a once-in-1,000-days loss of 16.21% cannot be smaller than that loss. The conclusion calls the EVT and CVaR estimates very accurate and realistic.

There are two other discrepancies. The methods express VaR as parametric μ + Zσ, whereas the results take the empirical 5th percentile. Both VaR and CVaR come from the full period in-sample; the paper gives no exceedance count for the -1.8684% line. The 1.12-point distance between VaR and CVaR is consistent with a fat left tail and kurtosis of 7.7658. The GPD parameters give a trader nothing usable for sizing.

Monte Carlo has its own source of optimism. The authors estimate drift from a sample with mean daily return of 0.0881% and total return of 194.43%. They attribute the difference between the 365-day weighted projection, USD 6,418.10 (+36.68%), and ARIMA's USD 5,453.14 (+16.13%) to compounding that positive drift. No basis is given for the 60/30/10 scenario weights. The scenario called "Ekstrem" COVID uses 1.16% volatility, below the geopolitical scenario's 1.50%.

What happened in our GLD run?

We could not trade the paper's futures series. We instead adapted the approach to daily GLD, the US-listed gold ETF. Its fees and tracking error prevent us from reproducing any of the paper's figures on it. At each close, our strategy fits ARIMA(1,1,1) to a three-year rolling window of adjusted closes and predicts the next close. It holds 100% GLD when that prediction exceeds the current close and a rolling peaks-over-threshold risk gate passes: estimated VaR loss under 2%, CVaR loss under 4%, and GPD shape under 1. Otherwise, it holds cash. GARCH serves only as a validity check. Our 100%-or-zero positions do not exercise the paper's proposed GARCH-based sizing.

From 2020-01-01 to 2024-07-01, the backtest earned 0.65% after per-share commissions, with a Sharpe of 0.01. Maximum drawdown reached -35.11%. It made 542 trades and won 45.76% of them. The paper's 9.15% MAPE measures 60-day price-level forecasts from December 2024 to April 2026; it reports no trading return to compare with ours. We use a different instrument and metric, over a window that does not overlap.

Some of the poor showing has plausible sources. The paper scores 60-day forecasts during a rally; our positions follow one-session forecasts. Its Ljung-Box p of 0.5598 suggests little one-day linear predictability. Our window includes the COVID and consolidation phases, for which the paper reports gold futures drawdowns of 18.33% and 20.54%. Around a forecast close to drift, 542 trades likely meant whipsaw. The tail gate may also have put the strategy in cash during volatile rebounds. The paper's full-sample GPD shape of 1.50 would fail our gate outright.

Execution adds another uncertainty. The design called for next-open fills, but the run recorded close-auction fills. The effect of that mismatch could go either way.

The drawdown remains unexplained. Although the book spent part of the period in cash, it had 13.16% annualized volatility and lost -35.11% at its worst point. That exceeds the paper's largest reported gold futures phase drawdown of 20.54%. The instruments differ, and those phase figures describe a passive position; the comparison establishes only that our gates failed to cap losses. This was one automated pass, evidence about our implementation before it is evidence about the authors' models.

The error row that matters

An out-of-sample, one-step daily test would put ARIMA beside no-change and drift-only forecasts on the same closes. GARCH conditional volatility would determine position size, as the paper proposes, and the test would charge costs. Until ARIMA clears the drift line, its 9.15% MAPE largely measures windows within a phase when gold gained 126.47%. The GPD shape of 1.50 also rules out using those tail estimates for limits. A random-walk error row showing ARIMA clearly ahead at the 60-day horizon would change my view. The authors have the inputs to produce it.

Our backtest stops at 2024-07-01, and everything after that date is deliberately left untouched so the same strategy can be checked out of sample later.

At each session close, take the latest 756 valid adjusted closes.
If history is insufficient, remain in cash.
Fit ARIMA(1,1,1) to prices; forecast the next close.
Fit GARCH(1,1) to rolling log returns and require valid, finite variance and persistence < 1.
Set u to the rolling fifth-percentile log return. Require at least 30 returns r < u; fit a valid GPD to excesses u − r.
Controlling VaR loss = −u; controlling CVaR loss = −u + fitted_scale / (1 − fitted_shape). Require fitted_shape < 1.
Target 100% GLD only if forecast_close > decision_close, VaR loss < 2%, CVaR loss < 4%, and all required estimates are valid; otherwise target cash.
On a target change, the specification calls for execution at the next available adjusted open; hold until a later target change.
Record the no-drift random-walk forecast and other diagnostics separately from entry signals.