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 grangercausalitytests  n = 1000 ls = np.linspace(0, 2*np.pi, n)  df1 = pd.DataFrame(np.sin(ls)) df2 = pd.DataFrame(2*np.sin(1+ls))  df = pd.concat([df1, df2], axis=1)  df.plot()  grangercausalitytests(df, maxlag=20) 

However, I am getting

Granger Causality number of lags (no zero) 1 ssr based F test:         F=272078066917221398041264652288.0000, p=0.0000  , df_denom=996, df_num=1 ssr based chi2 test:   chi2=272897579166972095424217743360.0000, p=0.0000  , df=1 likelihood ratio test: chi2=60811.2671, p=0.0000  , df=1 parameter F test:         F=272078066917220553616334520320.0000, p=0.0000  , df_denom=996, df_num=1  Granger Causality number of lags (no zero) 2 ssr based F test:         F=7296.6976, p=0.0000  , df_denom=995, df_num=2 ssr based chi2 test:   chi2=14637.3954, p=0.0000  , df=2 likelihood ratio test: chi2=2746.0362, p=0.0000  , df=2 parameter F test:         F=13296850090491009488285469769728.0000, p=0.0000  , df_denom=995, df_num=2 ... /usr/local/lib/python3.5/dist-packages/numpy/linalg/linalg.py in _raise_linalgerror_singular(err, flag)      88       89 def _raise_linalgerror_singular(err, flag): ---> 90     raise LinAlgError("Singular matrix")      91       92 def _raise_linalgerror_nonposdef(err, flag):  LinAlgError: Singular matrix 

and I am not sure why this is the case.

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.