Self-Forecast Feedback: Mechanisms & Insights

• Self-forecast feedback is a process where a model’s own forecasts, actions, or errors reenter the prediction loop to influence future outcomes.
• It involves distinct mechanisms such as outcome, state, error, and prediction feedback which address bias, endogeneity, and shifting data distributions.
• Applications span time-series improvements to self-refinement in AI, highlighting challenges in causal inference, deployment risk, and system stability.

Searching arXiv for papers relevant to self-forecast feedback in forecasting and feedback-driven prediction. “Self-forecast feedback” (Editor’s term) denotes forecasting regimes in which a model’s own forecasts, forecast-induced actions, or realized forecast errors re-enter the system that produces later observations, supervisory signals, or correction terms. In current research, this umbrella covers at least four distinct mechanisms: forecasts that alter the target process through policy or performativity, recursive rollout that moves a predictor onto self-generated states, rolling-error feedback that corrects subsequent forecasts using residual histories, and forecast-augmentation schemes that reuse model-generated predictions as auxiliary context. Across these strands, the shared technical issue is endogeneity: once forecasts influence either the future data or the state on which later predictions are made, passive evaluation and one-shot training objectives need not characterize deployed behavior (Lieli et al., 2023, Zhao et al., 2023, Green et al., 11 Jun 2026, Schmitt, 13 May 2026).

1. Mechanistic taxonomy

A useful way to organize self-forecast feedback is by the object that feeds back. In some models, the forecast changes an external action, and the action changes the realized target. In others, the forecast changes the internal state visited during recursive rollout. A third class uses historical forecast errors as explicit corrective inputs. A fourth reuses model-generated future predictions as augmentation for a second-stage forecaster.

Mechanism family	Feedback carrier	Representative formulation
Outcome feedback	Forecast-induced action or policy	$y_{t+1}=\theta_t+a_t+\epsilon_{t+1}$
State feedback	Self-generated induced states during rollout	$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$
Error feedback	Historical rolling residuals	$$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$
Prediction feedback	Model-generated future predictions reused as inputs	$$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$

These families are not interchangeable. Outcome feedback is causal and environmental; state feedback is endogenous to recursive deployment; error feedback is retrospective and corrective; prediction feedback is anticipatory and architectural. This suggests that “feedback” in forecasting is not a single phenomenon but a family of closure mechanisms with different observability, identifiability, and stability properties (Green et al., 11 Jun 2026, Huang et al., 26 Feb 2026, Kim et al., 2 Feb 2026).

2. Forecasts as interventions: policy feedback and performativity

In “Forecasting with Feedback,” the forecast is explicitly part of the data-generating process. The forecaster observes information summarized by $\theta_t=g(I_t)$ and issues a point forecast $f_t$ for $y_{t+1}$, but the outcome depends on both the state and the decision maker’s action:

$y_{t+1}=\theta_t+a_t+\epsilon_{t+1}.$

With quadratic loss, the forecaster solves

$$\min_{f_t} E\left\{[\theta_t+a(f_t)+\epsilon_{t+1}-f_t]^2\mid\theta_t\right\}.$$

The key departure from standard forecasting is that the variance term itself depends on the forecast because the forecast affects policy. Under uncertainty about the policy reaction strength, the optimal forecast becomes attenuated relative to the unbiased conditional-mean rule, and the optimal slope can be written as a shrunken version of the unbiased slope:

$$e^*=\lambda\cdot \frac{c}{\mu+c},\qquad \lambda=\frac{(\mu+c)^2}{\tau^2+(\mu+c)^2}\in(0,1).$$

The paper’s central result is that systematic forecast bias can be optimal even under quadratic loss; the equilibrium bias is

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$0

This directly challenges the common interpretation of bias as irrationality. The same framework also shows that standard Mincer–Zarnowitz implications can fail: the intercept need not be zero, the slope need not be one, and forecast errors need not be orthogonal to information (Lieli et al., 2023).

“Performative Time-Series Forecasting” generalizes the same intuition to machine-learning time series. It formalizes performative time-series forecasting (PeTS), where predictions can influence the predicted outcome and thereby alter the target distribution, producing “self-negating” or “self-fulfilling” forecasts. The proposed Feature Performative-Shifting (FPS) method leverages delayed response to anticipate performativity-induced distribution shifts. Theoretical analysis suggests that FPS can reduce generalization error, and experiments with multiple time-series models on COVID-19 and traffic forecasting show that FPS consistently outperforms conventional time-series forecasting methods (Zhao et al., 2023).

Taken together, these works establish a strong version of self-forecast feedback: the forecast is not merely an estimate of an exogenous future, but an endogenous signal that changes the future it is evaluated against.

3. Recursive rollout and self-induced state regimes

A different form of self-forecast feedback appears in recursive multi-step forecasting. “Exposure Bias as Epistemic Underidentification in Recursive Forecasting” argues that recursive rollout is not only a distribution-shift problem. Under partial observability or state truncation, it is also an epistemic underidentification problem: one-step Bayes supervision identifies behavior on observed contexts but need not identify the deployed recursive predictor on self-generated induced states (Green et al., 11 Jun 2026).

The paper formalizes the observed support as

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$1

defines the recursive transition

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$2

and the two-step recursive forecast

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$3

Its core theorem states that if a Bayes-optimal one-step predictor maps some observed state $$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$4 to an induced state outside observed support, then one-step Bayes optimality does not determine recursive rollout there. Concretely, the paper constructs two predictors $$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$5 such that

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$6

but

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$7

This means that predictors indistinguishable on the observed training distribution can diverge under self-generated rollout.

To describe the local prediction problem induced by rollout, the paper introduces induced states and provenance:

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$8

so that the relevant correction task becomes

$$T_g(x_1,\ldots,x_{\hat p})=\bigl(g(x_1,\ldots,x_{\hat p}),x_1,\ldots,x_{\hat p-1}\bigr)$$9

The associated induced-state error decomposes into three nonnegative parts: teacher-forcing/rollout mismatch, representation–class gap, and provenance gap. The provenance term is

$$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$0

This formalizes the claim that the same numeric induced state may require different local corrections depending on how that state was produced.

The toy delay-system example makes the point concrete: the same numeric state $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$1 appears both as an observed context and as an induced rollout state, but the correct local target differs, with observed $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$2 and induced $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$3. A binary provenance tag disambiguates the two. Empirically, a linear probe increasingly distinguishes observed contexts from teacher-forced induced states as rollout depth grows; fixed induced states define a distinct local corrective task; and full closed-loop gains arise partly from local correction and partly from changing the induced states visited during rollout. Provenance-aware correction is helpful only conditionally, and the simple binary provenance encoding is described as suggestive but weak (Green et al., 11 Jun 2026).

The broader implication is that self-forecast feedback can be a state-creation mechanism. The model is not only predicting on shifted inputs; it is partly creating the regimes on which later predictions must operate.

4. Residual feedback, look-ahead augmentation, and future-guided correction

A large engineering literature studies self-forecast feedback as an internal correction channel. In “TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series,” the correction signal is the model’s own historical residuals from rolling forecasts. The core formulation is

$$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$4

where $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$5 is the base forecaster and $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$6 is an error-feedback module. For multi-horizon forecasting under partial observability, TEFL uses the complete residual vector from exactly one horizon ago:

$$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$7

Residuals are injected through a low-rank adapter,

$$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$8

with $$\hat{y}_t = f([y_{t-1}, \ldots, y_{t-p}]) + g([e_{t-1}, \ldots, E_{t-q}])$$9 and $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$0. Training proceeds in two phases: a warm-up stage with a composite loss that includes spectral flatness of the residual sequence, followed by joint training with causal error simulation over contiguous windows. Across 10 real-world datasets and 5 backbones, TEFL reduces MAE by about 5–10% on average, and under shocks or progressive drift the reported error reductions exceed 10%, reaching up to 19.5% in challenging scenarios (Huang et al., 26 Feb 2026).

“Back to the Future” implements a different corrective loop. A first-stage direct multi-step model generates

$$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$1

the forecast is partitioned into segments, and each segment is appended to the original input:

$$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$2

Second-stage models are then trained independently on the augmented inputs, and their outputs are ensembled with a variance/correlation-based top-$$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$3 selection rule. The paper characterizes this as look-ahead augmentation and self-corrective refinement. Reported gains reach 58.7% MSE improvement on ILI at horizon 24 for Linear + BTTF (1E-1E), with stable improvements even when the first-stage model is trained under suboptimal conditions (Kim et al., 2 Feb 2026).

“Future-Guided Learning” uses a temporally offset teacher–student architecture rather than a residual adapter. A detection or next-step teacher model, trained on later or more informative data, supervises a forecasting student through a combined objective that mixes supervised loss with a time-offset KL divergence between teacher and student outputs. The paper interprets this through predictive coding and surprise minimization, with larger teacher–student discrepancies producing larger corrective updates. Reported results include a 44.8% increase in AUC-ROC for seizure prediction using EEG data and a 48.7% reduction in MSE for forecasting in nonlinear dynamical systems; on Mackey Glass, gains are stronger at longer horizons (Gunasekaran et al., 2024).

An earlier statistical variant appears in the wind-power literature. “Grid-scale Fluctuations and Forecast Error in Wind Power” analyzes generated and forecast Irish grid wind-power series, identifies correlated fluctuations with self-similar structure, and defines a timescale error $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$4 and a scaling error $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$5. Without any a priori knowledge of the forecast model, it proposes an exponential memory-kernel correction,

$$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$6

tuned to better match the correlation structure of generated power. The modified forecast restores short-time scaling and reduces the scaling mismatch, with the corrected exponent reported as $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$7 (Bel et al., 2015).

These approaches differ in architecture but share a common premise: the model’s own outputs or output errors contain structured information that can be causally reused for correction rather than discarded as mere post hoc evaluation.

5. Historical risk, deployment risk, and identifiability

Self-forecast feedback makes evaluation nontrivial because the forecasting model becomes part of the environment it is supposed to predict. “Algometrics: Forecasting Under Algorithmic Feedback” formalizes this distinction by separating passive historical risk from deployment risk. Given a forecaster $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$8 and a deployment map $$\mathbf{x}^{(i)}_{\mathrm{aug}} = \left[\mathbf{x}_{t-L+1:t};\; \hat{\mathbf{x}}^{(1)}_{\mathrm{seg}, i}\right]$$9, historical risk is

$\theta_t=g(I_t)$0

where $\theta_t=g(I_t)$1 is the passive law, while deployment risk is

$\theta_t=g(I_t)$2

The feedback gap is

$\theta_t=g(I_t)$3

This distinction is the paper’s central evaluative claim: a model can look strong under passive historical testing yet behave differently once its forecasts drive actions (Schmitt, 13 May 2026).

The paper’s main impossibility result is non-identifiability from passive data alone. In the one-step linear feedback model

$\theta_t=g(I_t)$4

the passive regime sets $\theta_t=g(I_t)$5, so passive data identify $\theta_t=g(I_t)$6 but not $\theta_t=g(I_t)$7. Yet deployment risk for a fixed forecaster becomes a nonconstant quadratic function of $\theta_t=g(I_t)$8. Consequently, no estimator based only on passive histories can identify deployment risk uniformly over that family. A second result shows ranking inversion under crowding. With passive target $\theta_t=g(I_t)$9 and deployed target

$f_t$0

historical risk is

$f_t$1

while deployment risk is

$f_t$2

Thus the passive-best predictor can become worse than a more conservative predictor once adoption is sufficiently large. A positive result follows: randomized or instrumented actions identify short-horizon linear feedback and permit finite-sample deployment-risk bounds (Schmitt, 13 May 2026).

This feedback-aware view aligns with the rationality critique in policy-feedback models. Under forecast-dependent policy response, Mincer–Zarnowitz tests need not have zero intercept or unit slope, so traditional signs of “irrationality” can arise even when the forecast is fully optimal under quadratic loss (Lieli et al., 2023).

A persistent misconception is therefore that passive predictive accuracy and deployment quality are interchangeable. The literature instead indicates that self-forecast feedback can alter both the target law and the state visitation distribution, so historical backtesting may estimate the wrong object.

6. Limitations, misconceptions, and adjacent self-feedback paradigms

Current work also makes clear that self-feedback is not uniformly reliable. “A Study on Leveraging Search and Self-Feedback for Agent Reasoning” examines the use of search and model-generated feedback for reasoning tasks and reports challenges related to generalization when solely relying on self-feedback during search. Its conclusion is explicit: for search to work effectively, either access to the ground truth is needed or feedback mechanisms need to be carefully designed for the specific task (K et al., 17 Feb 2025).

That caution is consistent with the forecasting papers. In recursive forecasting, provenance-aware correction is mixed rather than uniformly helpful; in TEFL, the simple low-rank adapter outperforms heavier fusion modules; in BTTF, gains can be small or slightly negative when the first-stage model is already well fitted; and in policy/performative settings, feedback can induce bias, ranking inversion, or non-identifiability rather than improvement. A plausible implication is that self-forecast feedback should be understood less as an intrinsic advantage than as a design problem in causal observability, task structure, and stability.

Adjacent self-feedback systems outside time-series forecasting reinforce this design perspective. “Self-Refine” uses the same LLM as generator, feedback provider, and refiner, with iterative feedback improving outputs by roughly 20 percentage points absolute on average across seven tasks (Madaan et al., 2023). “Volcano” mitigates multimodal hallucination through a critique–revise–decide loop grounded in visual feedback (Lee et al., 2023). “SELF” trains self-feedback and self-refinement as meta-skills and then uses iterative self-evolution on unlabeled instructions (Lu et al., 2023). “Online Preference-based Reinforcement Learning with Self-augmented Feedback from LLM” replaces a scripted teacher with LLM preference labels, double-checking, and self-augmented imagined trajectories in online PbRL (Tu et al., 2024). “LLMs are Superior Feedback Providers” shows a suggestion–feedback collection–modification pipeline for lie detection in Diplomacy, with GPT-4-generated feedback outperforming expert human feedback and improving lying-F1 by 38.7% over the zero-shot baseline (Banerjee et al., 2024).

These systems are not forecasting models in the narrow time-series sense, but they instantiate the same high-level pattern: a model produces a provisional output, derives a structured signal from that output or its consequences, and reuses the signal for revision or learning. The forecasting literature adds a stronger constraint: because the feedback channel often changes the future data-generating process itself, the central questions are not only how to refine predictions, but also how to define the correct risk, how to preserve causality, and how to distinguish beneficial correction from self-induced distortion.