Error-by-Horizon Plot Calculator

Compare forecasting errors across horizons, evaluate multiple models, inspect uncertainty and bias, identify performance changes, and export clear diagnostic reports for better decisions quickly.

Forecast Error Results

Results appear here after analysis.

Not calculated
Load sample data or enter your own forecasts.
Horizon Model Count Mean Error MAE MSE RMSE MAPE sMAPE Bias Std. Dev. CI Status

1. Data Input

Actual mode requires horizon, actual, and one or more model columns. Precomputed mode requires horizon, model, and error.

2. Metrics and Aggregation

3. Horizon Configuration

4. Confidence, Variability, and Smoothing

5. Baseline, Threshold, and Classification

6. Filtering and Outlier Handling

7. Plot Customization

Formula Used

Error: e(h) = Actual(h) − Forecast(h)
MAE(h) = Σ|eᵢ(h)| / n(h)
MSE(h) = Σeᵢ(h)² / n(h)
RMSE(h) = √MSE(h)
MAPE(h) = [Σ|eᵢ(h) / Actualᵢ(h)| / n(h)] × 100
sMAPE(h) = [Σ 2|eᵢ(h)| / (|Actualᵢ(h)| + |Forecastᵢ(h)|) / n(h)] × 100
Bias(h) = Σeᵢ(h) / n(h)

How to Use

Enter forecast horizons, actual values, and model predictions. Choose an error metric and grouping options. Then run the analysis to compare performance.

Use filters to isolate models, groups, or origins. Configure confidence bands and outlier handling carefully. Export the table or chart for reporting.

  1. Load the sample data or paste a CSV dataset.
  2. Select the main metric shown on the plot.
  3. Choose confidence, smoothing, threshold, and filtering options.
  4. Click Analyze Forecast Errors.
  5. Review summaries, diagnostics, charts, and horizon tables.

Example Data

HorizonActualNaiveModel AModel B
1120116118121
2125119122124
3130122126128
4135126129133
5140129132137

Interpretation Guide

A rising curve means forecasts become less accurate farther ahead. A flat curve indicates stable performance across horizons. Large bands show uncertain or inconsistent forecast errors.

Positive mean error indicates forecasts are generally too low. Negative mean error indicates forecasts are generally too high. Compare models using identical horizons and observations.

Frequently Asked Questions

What is an error-by-horizon plot?

It shows forecast error for each prediction distance. The horizontal axis contains forecast horizons. The vertical axis contains a selected error metric.

Why does forecast error often increase?

Longer forecasts depend on more uncertain future conditions. Small assumptions can compound over multiple steps. Wider horizons therefore often produce larger errors.

Which error metric should I use?

MAE is easy to interpret in original units. RMSE penalizes large mistakes more strongly. Percentage metrics help compare series with different scales.

Can multiple models be compared?

Yes, add one column for each model. Every model appears as a separate plot series. The table also reports horizon-level performance.

What do confidence bands show?

They summarize uncertainty around the aggregated error estimate. Narrow bands indicate more stable observed errors. Wide bands indicate variability or limited observations.

How are zero actual values handled?

MAPE excludes observations with zero actual values. sMAPE remains available in many zero-value situations. Warnings identify any excluded percentage calculations.

Should outliers be removed?

Remove outliers only with a defensible reason. Extreme errors may reveal genuine model weaknesses. Compare filtered and unfiltered results before deciding.

What is forecast bias?

Bias is the average signed forecast error. Positive bias means forecasts are generally too low. Negative bias means forecasts are generally too high.

Can the chart be exported?

Yes, download PNG or SVG chart files. Export the results table as CSV. Print the page to create a PDF report.

Related Calculators

Time-Series Line ChartRolling Mean PlotRolling Standard-Deviation PlotSeasonal Decomposition PlotAutocorrelation Plot (ACF)Partial Autocorrelation Plot (PACF)Lag PlotForecast-versus-Actual PlotForecast Confidence-Band PlotSeasonal Subseries Plot

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.