Why is the tuple index out of range in the generation of timeseries with tigramite library?

I have installed the tigramite package for causal inference and imported the following libraries:

# Imports
import numpy as np
import matplotlib
from matplotlib import pyplot as plt
%matplotlib inline     
import sklearn

import tigramite
from tigramite import data_processing as pp
from tigramite.toymodels import structural_causal_processes as toys

from tigramite import plotting as tp
from tigramite.pcmci import PCMCI
from tigramite.lpcmci import LPCMCI

from tigramite.independence_tests.parcorr import ParCorr
from tigramite.independence_tests.robust_parcorr import RobustParCorr
from tigramite.independence_tests.parcorr_wls import ParCorrWLS 
from tigramite.independence_tests.gpdc import GPDC
from tigramite.independence_tests.cmiknn import CMIknn
from tigramite.independence_tests.cmisymb import CMIsymb
from tigramite.independence_tests.gsquared import Gsquared
from tigramite.independence_tests.regressionCI import RegressionCI

Now I have found the following code to generate and simulate time series:

np.random.seed(42)     # Fix random seed to make results reproducible
links_coeffs = {0: [((0, -1), 0.7), ((1, -1), -0.8)],
            1: [((1, -1), 0.8), ((3, -1), 0.8)],
            2: [((2, -1), 0.5), ((1, -2), 0.5), ((3, -3), 0.6)],
            3: [((3, -1), 0.4)],
            } #stores the coefficients of the SCM
 T = 1000     # time series length
 #generate the timeseries
 data, true_parents_neighbors = toys.structural_causal_process(links_coeffs, T=T) 
 T, N = data.shape

 # Initialize dataframe object, specify time axis and variable names
 var_names = [r'$X^0$', r'$X^1$', r'$X^2$', r'$X^3$']
 dataframe = pp.DataFrame(data, 
                     datatime = {0:np.arange(len(data))}, 
                     var_names=var_names)

However I got IndexError: tuple index out of range coming, probably from the line to generate the time series data, true_parents_neighbors = toys.structural_causal_process(links_coeffs, T=T)

How can I solve it?

That's because of the format of your links_coeffs.

To use structural_causal_process, the links must have the format {0:[((i, -tau), coeff, func),...], 1:[...], ...}, which don't match the one you specify. Correct links would look like this :

def fn(x):
    return x

links_coeffs = {
    0: [((0, -1), 0.3, fn), ((2, 0), 0.5, fn), ((3, -1), -0.5, fn)],  # X1
    1: [((1, -1), 0.3, fn)],  # X2
    2: [((2, -1), 0.3, fn), ((1, -2), 0.4, fn)],  # X3
    3: [((3, -1), 0.3, fn)],  # X4
}

If you need that specific format of links, then maybe you should consider using var_process :

data, true_parents_neighbors = toys.structural_causal_process(links_coeffs, T=T)
data, true_parents_neighbors = toys.var_process(links_coeffs, T=T)