Why am I getting “LinAlgError: Singular matrix” from grangercausalitytests?

Question

I am trying to run grangercausalitytests on two time series:

import numpy as np
import pandas as pd

from statsmodels.tsa.stattools import grang         


        

Answer 1

The problem arises due to the perfect correlation between the two series in your data. From the traceback, you can see, that internally a wald test is used to compute the maximum likelihood estimates for the parameters of the lag-time series. To do this an estimate of the parameters covariance matrix (which is then near-zero) and its inverse is needed (as you can also see in the line invcov = np.linalg.inv(cov_p) in the traceback). This near-zero matrix is now singular for some maximum lag number (>=5) and thus the test crashes. If you add just a little noise to your data, the error disappears:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import grangercausalitytests

n = 1000
ls = np.linspace(0, 2*np.pi, n)
df1Clean = pd.DataFrame(np.sin(ls))
df2Clean = pd.DataFrame(2*np.sin(ls+1))
dfClean = pd.concat([df1Clean, df2Clean], axis=1)
dfDirty = dfClean+0.00001*np.random.rand(n, 2)

grangercausalitytests(dfClean, maxlag=20, verbose=False)    # Raises LinAlgError
grangercausalitytests(dfDirty, maxlag=20, verbose=False)    # Runs fine

Answer 2

Another thing to keep an eye out for is duplicate columns. Duplicate columns will have a correlation score of 1.0, resulting in singularity. Otherwise, it's also possible you have 2 features that are perfectly correlated. And easy way to check this is with df.corr(), and look for pairs of columns with correlation = 1.0.