# Linear granger causality

## Algorithm Introduction

Implementation of granger causality 1, including 1) regression+hypothesis test and 2) lasso regression 2.

## Usage

```
from causallearn.search.Granger.Granger import Granger
G = Granger()
p_value_matrix = G.granger_test_2d(data)
coeff = G.granger_lasso(data)
```

## Parameters

**data**: numpy.ndarray, shape (n_samples, n_features). Data, where n_samples is the number of samples
and n_features is the number of features. Note that for granger_test_2d(), the shape of input data is (n_samples, 2).

## Returns

**p_value_matrix**: p values for x1->x2 and x2->x1 (for ‘granger_test_2d’, which is the granger causality test for two-dimensional time series).

**coeff**: coefficient matrix (for ‘granger_lasso’, which is the granger causality test for multi-dimensional time series).

- 1
Granger, C. W. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: journal of the Econometric Society, 424-438.

- 2
Shojaie, Ali, and George Michailidis. “Discovering graphical Granger causality using the truncating lasso penalty.” Bioinformatics 26.18 (2010): i517-i523.