STI graph forecasts need an interval benchmark against GARCH

A 50.76% hit rate over 331 days of Straits Times Index returns gives a trader a coin flip. The authors acknowledge that. Their case rests instead on changing graph connections and adaptive prediction intervals. Neither faces a GARCH-type volatility model or a static-graph version of the same system in the paper's tests.

Inside the forecast

Le Binh Trung and his co-authors use a four-node daily system. Its inputs are the STI log return, the USD/SGD log return, the VIX in levels and the S&P 500 log return.

A small feed-forward network takes those four standardized values each day and produces a 4x4 matrix of edge probabilities. Self-loops are excluded. This is the time-varying stochastic graph: its connections change with the inputs. Training samples the edges through a logistic relaxation at temperature 0.5, allowing the random graph to remain differentiable. Testing uses the raw probabilities directly.

The graph is row-normalized and mixes the nodes before a nonlinear layer transforms the result. This process repeats across a 20-trading-day window, whose sequence an LSTM with hidden dimension 64 then reads. Two output heads estimate tomorrow's STI return mean and standard deviation. Gaussian negative log-likelihood trains the entire system.

Yahoo Finance closes supply 2,544 aligned days from January 2015 to July 2026. The training period is 2015 to 2023 (1,954 samples), followed by validation in 2024 (199). Testing covers January 2025 to July 2026 (331). The paper supplies no trading rule, Sharpe or cost model. Its possible economic value therefore lies in better conditional distributions for risk sizing.

Point forecasts draw level with a zero-return random walk. Both have MAE of 0.0054; RMSE is 0.0086 versus 0.0087. Interval coverage reaches 84.59% at nominal 80% and 93.66% at nominal 95%. The paper acknowledges the point-forecast result in its opening summary, then offers its defence: the model "produces time-varying graph connectivity and reasonably calibrated predictive intervals." That is the claim requiring a test.

Why does the US close add so little?

The RMSE improvement amounts to 0.0001. MAE matches at four decimals, and we found no Diebold-Mariano or similar test in the paper. The timing makes this stranger. On the same date, the S&P 500 closes in New York after Singapore has finished trading. Thus x_t already includes a US session the STI has yet to trade.

That overnight spillover is the dataset's most obvious potential source of next-day signal. Even with the US close among its inputs, however, the full model achieves directional accuracy of only 50.76%. Its RMSE is 0.0086, against the random walk's 0.0087.

The learned connections raise another question. During the 2025-2026 test period, the S&P 500 to STI edge averages 0.374, the lowest of the three incoming edges. The VIX averages 0.633 and USD/SGD 0.41. Those figures alone cannot establish that the model ignores the US leg: row normalization makes each weight relative. The S&P 500 feeds the USD/SGD row at 0.46 and the VIX row at 0.425 as well. It also enters the network determining every edge as one of its four inputs.

We found no discussion of asynchronous closes. With self-loops excluded and rows normalized, the STI node represents a weighted average of the other three nodes. The graph therefore makes it difficult to see how the STI's own lagged return reaches the forecast. Table 5 suggests a route back through the other rows. The STI is the strongest source feeding the S&P 500 node (0.693) and the VIX node (0.636).

The intervals have no opponent

The scale forecasts deserve some credit. Predicted standard deviation expands sharply around April 2025, then shrinks. Its Pearson correlation with the next day's absolute return is 0.3295; the Spearman correlation is 0.119 (p = 0.0307). The authors attribute some of that difference to extreme episodes. They call σ̂ "a model-implied measure of predictive uncertainty rather than as a precise forecast of subsequent absolute returns."

That concession has force. Much of the 0.33 Pearson figure comes from a few large-move days, especially April 2025. Smaller expansions later in the window also appear in the paper.

Coverage follows a familiar Gaussian pattern: the intervals over-cover at 80% and under-cover at 95%. A normal likelihood applied to fat-tailed returns produces just this problem. Across the full sample, the STI minimum of -7.75% lies more than nine standard deviations (0.844%) from the mean. The authors propose heavier-tailed or asymmetric conditional distributions as a possible extension.

Coverage by itself proves little about skill. Even a constant-width band based on unconditional quantiles can approach nominal coverage over 331 days. Sharpness matters: how narrow are the intervals at the coverage they achieve? The paper's random-walk results row has dashes for NLL and both coverage columns. Its test NLL of 1.3679 consequently has no benchmark. We found no reported interval width either.

GARCH(1,1) on STI returns, ideally with Student-t errors, is the first comparison needed. The stochastic connections then need two ablations to earn their place: a graph-free probabilistic LSTM using the same 20-day inputs, and the existing architecture with one fixed learned adjacency. A fixed graph matching the NLL would leave the changing connections in Fig. 2 as decoration. Table 5 cannot answer that question with averages. The paper itself says those averages hide variation through time; the fixed-graph ablation is needed to resolve it. There are also no sensitivity runs for hyperparameters such as τ = 0.5 or the 20-day window, and we found no reported variance across training seeds.

April 2025 carries much of the evidence

We could not rerun this.

Our data contains neither STI price history nor a USD/SGD spot series. We have the S&P 500 and VIX legs. Replacing the target with a US index and the currency node with a dollar proxy would, however, produce a different experiment.

The evidence therefore remains 331 Singapore trading days, with April 2025 contributing heavily to the Pearson figure. The authors identify the four-node system and Gaussian assumption as limitations, along with the one-day horizon and single market. They also write that "flexible nonlinear architectures cannot create predictable information when the conditional mean contains little exploitable signal." The same reasoning applies to the scale head. If a GARCH recursion already extracts that variance signal, the graph has created none of it.

One table would change my view: the graph model beating GARCH-t and a plain probabilistic LSTM on NLL or interval width over those same 331 days.