Granger Causality Tool Calculator

Calculator

Enter two aligned time series of equal length. Use the same time step for both series.

Data input method

CSV should contain two numeric columns (X then Y).

Direction

Null hypothesis: no predictive signal at chosen lag.

Significance level (α)

Common choices: 0.10, 0.05, 0.01.

Lag mode

Auto chooses the best lag within max lag.

Fixed lag

Used when lag mode is fixed.

Maximum lag

Upper bound for auto lag selection.

Criterion

Lower criterion value indicates better fit.

Include intercept

Add a constant term

Disable if your data is already centered.

Preprocessing options

First difference (Δ)

Demean (remove mean)

Standardize (z-score)

Input data

Tip: keep both series aligned by time index.

Series X *

Comma, space, or newline separated values.

Series Y *

If you upload CSV, pasted text is ignored.

CSV upload (optional)

CSV should have two numeric columns per row.

Example data table

This sample shows two short, aligned series. Replace with your own observations for real analysis.

Time	X	Y
1	1	1.2
2	2	1.9
3	3	3.4
4	4	3.8
5	5	5.1
6	6	5.9
7	7	7.2
8	8	7.9
9	9	9.4
10	10	9.8
11	11	11.1
12	12	12

CSV format example: X,Y with one row per time step.

Formula used

Granger testing compares a restricted model to an unrestricted model for a chosen lag L.

Restricted model (no X lags)

y_t = c + Σ_i=1..L a_i y_t−i + ε_t

Unrestricted model (adds X lags)

y_t = c + Σ_i=1..L a_i y_t−i + Σ_i=1..L b_i x_t−i + u_t

The F statistic is computed from the sum of squared errors (SSE):

F = ((SSE_R − SSE_U) / L) / (SSE_U / (n_eff − k_U))

SSE_R: restricted model error
SSE_U: unrestricted model error
n_eff: usable rows after lagging
k_U: unrestricted parameters (incl. intercept)

Reminder: “Granger causality” indicates predictive content in lags, not real-world cause and effect.

How to use this calculator

Enter aligned values for Series X and Series Y, or upload CSV.
Select direction (X → Y, Y → X, or both).
Choose lag mode: auto selection or a fixed lag.
Set α, then pick optional preprocessing if needed.
Press Run Test to view results above.
Use the download buttons to export CSV or PDF.

Practical tips: prefer stationary series, avoid over-large lags, and ensure enough observations. If results look unstable, try differencing or fewer lags.

What the test measures in time series

Granger testing asks whether past X improves prediction of Y. It compares a restricted regression using only lagged Y terms with an unrestricted regression that also includes lagged X terms. If the added X lags reduce error enough, the F statistic increases and the p-value decreases. Stationarity assumptions matter; treat trends carefully. This tool reports both directions so predictability can be checked symmetrically.

Lag choice and information criteria

Lag length defines how far back the model looks. Too few lags can miss delayed relationships, while too many lags consume degrees of freedom and overfit noise. Auto mode evaluates lags up to a maximum and selects the minimum AIC or BIC. AIC typically prefers more flexibility; BIC is stricter and often chooses shorter lags for small samples. Choose max lag using domain cycles and sampling rate.

Data alignment and preprocessing options

Use evenly spaced observations and align timestamps carefully, because misalignment can manufacture apparent predictability. Many series are non-stationary, so first differences can stabilize the mean. Demeaning and standardizing help when levels differ widely or when numerical scaling causes unstable estimates. If you difference, interpret results as changes, not levels. Remember that the effective sample size shrinks by the selected lag, so longer histories support more reliable tests.

Interpreting outputs beyond significance

A small p-value indicates that lagged X terms add predictive content at the chosen α threshold; it does not prove real-world cause. Read the F statistic together with df1 and df2 to understand how many restrictions were tested and how much data remained. Compare restricted and unrestricted R² to see the fit, and check whether conclusions persist across nearby lags. When many lags are explored, be cautious about false positives.

Reporting results and practical limits

When sharing results, report the sampling interval, preprocessing steps, and the lag strategy used. Include both directions and document whether an intercept was fitted. Granger conclusions can fail under omitted variables, structural breaks, shared trends, or regime shifts. For stronger evidence, pair this test with domain knowledge and additional diagnostics such as residual checks and stability plots. Exported reports help keep a clear trail.

FAQs

Does Granger causality prove real causation?

No. It only tests whether lagged values of one series improve prediction of another within the chosen model. Common drivers, feedback loops, and trends can create predictability without a direct causal mechanism.

How many data points should I use?

More is better. After lagging, the effective sample drops by the selected lag and model parameters. Aim for dozens of observations at minimum, and substantially more when testing larger lags or noisy data.

Should I difference or standardize my series?

If the series has strong trends or unit-root behavior, differencing can help approximate stationarity. Standardizing is useful when scales differ greatly and you want stable estimation. Interpret outputs based on the transformed data.

How do I choose the lag length?

Use domain knowledge first, then compare nearby lags. Auto selection with AIC or BIC can provide a reasonable starting point, but confirm that results are stable and degrees of freedom remain adequate.

Why do X → Y and Y → X results differ?

Direction matters because each regression predicts a different target. It is common to find predictive signal in one direction only, especially with delayed responses or asymmetric feedback. Testing both directions helps identify likely lead–lag structure.

Can this handle more than two variables?

This single-file calculator is bivariate. For multivariate Granger analysis, you would fit a vector autoregression and test joint restrictions across multiple predictors. Use dedicated econometrics software when you need that scope.