Residual error

As explained in Time Series Forecasting Using Foundation Models

A forecast residual is the difference between an actual value and its predicted value.

A forecast residual is the difference between an actual value and its predicted value. In N-BEATS, residual connections instead pass forward information that earlier blocks did not capture. section 3.2.2 section 2.2.2

Residuals support two forecasting operations:

• Calculate the absolute residual as a conformity score for uncertainty estimation. section 3.2.2
• Subtract a block’s backcast from its input so later N-BEATS blocks learn uncaptured information. section 2.2.2

Rolling-window forecasts

Generate predictions across historical cross-validation windows, compare them with known actual values, and take the absolute differences as conformity scores. section 3.2.2

Figure 3.6 Adding conformity scores for each window. Here, the conformity score is calculated as the absolute difference between the actual and predicted value.

Shows conformity scores calculated as absolute differences between actual and predicted values. section 3.2.2

How Time Series Forecasting Using Foundation Models covers it

How deep it goes

Defines the difference and demonstrates its use in cross-validation and N-BEATS residual connections.

Examples

Uses two cross-validation windows with a three-step horizon and absolute actual–predicted differences.

What it assumes

Assumes forecasts and actual values are available, while explaining residual calculation from those values.

What you can do after

Apply it via cross-validation to calculate conformity scores for conformal prediction intervals.

How it connects

Connects forecasting with cross-validation, conformal prediction, prediction intervals, backcasts, and residual connections.

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Also explained in

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  Statistics Every Programmer NeedsResidual error is the difference between an observed response and its value predicted by a fitted model.
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  Effective Data AnalysisA residual is the difference between an observed outcome and the value predicted by a fitted model.
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  Machine Learning System DesignThe difference between a model prediction and its corresponding true value, especially in regression and more broadly as a sample-wise prediction error.
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  Ensemble Methods for Machine LearningA residual is the discrepancy between an observed target and a model prediction, or the corresponding per-example loss gradient in gradient boosting.
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  Grokking Machine LearningA residual is the difference between an observed target label and a model's predicted target value.
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  Experimentation for EngineersA residual is the portion of an observed value that remains unexplained after subtracting a model estimate.
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  Statistics Slam DunkA residual is the difference between an observed response value and its fitted value in a statistical model.
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  Grokking StatisticsA residual is the difference between an observed response value and the value predicted by a fitted model.
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  Causal Inference for Data ScienceA residual is the difference between an observed value and its value predicted by a fitted model.
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  Outlier Detection in PythonA time-series residual is the portion of an observation remaining after modeled trend and seasonal components are removed.

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Related concepts

• gradient boostingused by · Gradient boosting is an ensemble-learning technique that sequentially adds predictive models, typically weak learners, to reduce a loss by fitting its gradient.
• sum of squarespart of · A sum of squares is a quantity obtained by squaring specified values, deviations, or residuals and adding the resulting squares.
• conformity scoreused by · A conformity score is a numerical measure of how atypical an observation is relative to a prediction, here computed as the absolute forecast residual.

This explainer was generated by Manning's knowledge graph from the text of Time Series Forecasting Using Foundation Models. The section links point to the parts of the book it draws on.