Signal Simplification Is Not Predictive Simplification: Diagnosing Residual Neural Forecasting in Short-Horizon Volatility

1 Introduction

• The study separates a first-stage model's forecasting role from its preconditioning role: smaller residual variance does not guarantee a more predictable target for the next learner.The paper calls this empirical pattern forecaster–preconditioner asymmetry.Source: §1 · p. 2
• The six-model design compares AR, MA, and ARIMA references with HAR-style, a raw-sequence Pure LSTM, and a residual-only HAR-style+LSTM hybrid.Forecasts are evaluated chronologically using rolling-origin practice.Source: §1 · p. 2
• 0.3049 to 0.3594: residual-only HAR-style+LSTM MSE rises on all five assets, while Pure LSTM reaches 0.2649 and the residual hybrid has higher runtime.HAR-style residuals are strongly compressed, but that simplification does not yield better downstream neural forecasting.Source: §1 · p. 2
• The analysis asks whether a volatility-aligned first stage forecasts credibly and simplifies residuals, whether that simplification helps residual learning, and whether augmentation improves accuracy–efficiency trade-offs.The contribution separates signal transformation, downstream predictive value, and system cost, distinguishing fitted training residuals from rolling forecast errors.Source: §1 · pp. 2–3

2.1 Volatility Persistence and HAR-Style Forecasting

• HAR-RV captures long-memory-like volatility behavior through heterogeneous horizons and remains a standard forecasting benchmark; this study adapts that structure to intraday bars.The specification uses current-, three-, and six-observation components aligned with the rolling target.Source: §2.1 · p. 3

2.2 Neural and Residual Hybrid Forecasting

• Prior work combines statistical and neural models, but final hybrid accuracy does not isolate whether residualization creates a more learnable target.The study uses residual-only learning to assess predictive content retained in transformed residuals separately from additional contextual inputs.Source: §2.2 · pp. 3–4

2.3 Forecast Evaluation

• Rolling-origin evaluation preserves temporal ordering; the study reports MSE, MAE, benchmark-relative out-of-sample R2, and QLIKE, alongside Diebold–Mariano comparisons with Newey–West variance estimation.QLIKE is used for volatility comparisons with imperfect proxies.Source: §2.3 · p. 4

3.1 Preconditioning as a Forecasting Intervention

• Residual-LSTM training sequences use in-sample fitted residuals, while deployment history adds realized one-step-ahead errors only after their targets are observed.The hybrid adds a forecast of the residual to the first-stage forecast; it helps only if the downstream model predicts residuals better than leaving the first-stage forecast uncorrected.Source: §3.1 · p. 4

3.2 Forecaster–Preconditioner Asymmetry

• A first-stage model can reduce total residual variance while also reducing predictable residual variation, so a smaller residual need not be easier to forecast.The paper terms the empirical case of strong first-stage forecasting and residual simplification without beneficial downstream learning forecaster–preconditioner asymmetry.Source: §3.2 · p. 5

3.3 Signal, Forecast, and System Diagnostics

• Signal diagnostics measure residual variance reduction and lag-1 autocorrelation on fitted training residuals and sequential pseudo-out-of-sample errors as distinct objects.Forecast diagnostics include MSE, MAE, benchmark-relative R2, QLIKE, and paired Diebold–Mariano comparisons; system diagnostics compare predictive loss with end-to-end wall-clock cost.Source: §3.3 · pp. 5–6
• A hybrid with higher loss and higher cost is dominated in the measured implementation; runtime is treated as an implementation-level operational measure.The framework evaluates system cost alongside forecast loss rather than inferring value from residual simplification alone.Source: §3.3 · p. 6

4.1 Data and Target

• Five assets use 60-minute bars from January 2020 through January 2023; the target is next-bar six-observation rolling variance, with windows crossing session boundaries.Adjacent targets share five squared-return components, so their short-lag persistence reflects both volatility dynamics and target construction.Source: §4.1 · pp. 6–7

4.2 Models and Experimental Roles

• AR(5), MA(5), and ARIMA(1,0,1) are fixed references; HAR-style uses current, three-, and six-bar inputs, while LSTM variants test raw versus residual sequences.HAR coefficients are estimated by ordinary least squares, and the residual LSTM receives residual history without the original volatility state or first-stage forecast.Source: §4.2 · pp. 7–8

4.3 Rolling Protocol and Model Selection

• Chronological one-step forecasts use a 60% initial window and six-observation refits; neural architectures are selected retrospectively by rolling MSE across three seeds.Forecasts are generated sequentially within each refitting block, and newly observed targets can enter later inputs while parameters remain fixed until the next update.Source: §4.3 · p. 8

4.4 Computational Environment and Cost Measurement

• End-to-end wall-clock runtime covers the rolling runner's repeated fitting or updating and forecasts; reported measurements are hardware-specific and exclude architecture-search cost.For HAR-style+LSTM, the runner includes HAR refitting, residual construction, neural updating, and forecast recombination.Source: §4.4 · pp. 8–9

5.1 First-Stage Forecasting Validity

• HAR-style achieves MSE 0.3049 versus AR (0.5785), MA (0.5421), and ARIMA (0.5854); Pure LSTM records the lowest selected pseudo-out-of-sample MSE, 0.2649.Pure LSTM also has the lowest MSE on all five assets.Source: §5.1 · pp. 9–10, Figure 1 · p. 9, Table 1 · p. 9

5.2 Statistical Signal Simplification

• Fitted residual variance falls 81.95% with mean ACF(1) 0.0089; rolling HAR-style errors show 74.44% variance reduction and mean ACF(1) −0.0247.Neither residual object is white noise: mean ACF(6) is −0.3504 for fitted residuals and −0.3702 for rolling errors.Source: §5.2 · p. 10, Table 2 · p. 11, Figure 2 · p. 11

5.3 Forecaster–Preconditioner Asymmetry

• MSE rises from 0.3049 to 0.3594 with HAR-style+LSTM, an increase of 17.9%; the hybrid is worse on every asset.The increase ranges from 0.0372 for SPY to 0.0663 for XOM.Source: §5.3 · p. 11, Figure 3 · p. 12, Table 3 · p. 12

5.4 Accuracy–Efficiency Trade-off

• HAR-style+LSTM takes 353.12 seconds and produces MSE 0.3594, versus 2.87 seconds and MSE 0.3049 for HAR-style and 336.40 seconds and MSE 0.2649 for Pure LSTM.The hybrid is less accurate than Pure LSTM while retaining neural-scale runtime.Source: §5.4 · pp. 13–14, Figure 4 · p. 14, Table 6 · p. 14

• The standardized residual history produces less accurate forecasts than either HAR-style alone or Pure LSTM.Source: §6 · p. 15
• The diagnostics identify a pipeline-level contrast but do not uniquely decompose which information the first stage removes or retains.Source: §6 · p. 15
• The residual-only design does not test whether original volatility state, first-stage forecasts, or cross-asset information can recover value after residualization.Source: §6 · p. 15
• The evaluation covers five U.S. assets from 2020–2023 using a single-layer univariate LSTM family and retrospectively selected configurations.Source: §6 · p. 15
• Evaluating the transformed signal alongside downstream loss and system cost makes the information handoff explicit.Source: §6 · p. 15

• 0.3049 to 0.3594 mean MSE: residual-only LSTM augmentation worsens HAR-style forecasts, with higher error on all five assets.Source: §7 · p. 16
• Pure LSTM achieves the lowest selected pseudo-out-of-sample MSE, 0.2649.Source: §7 · p. 16
• A strong first-stage forecast and substantial residual simplification do not guarantee a representation that benefits downstream neural correction.Source: §7 · p. 16
• HAR-style is the low-cost statistical solution, Pure LSTM the strongest predictive solution, and HAR-style+LSTM combines neural-scale runtime with higher forecast error.Source: §7 · p. 16