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I write this message because I have a problem with cointegration and causality tests on R.
 
I'm working with time series data. I use ucra and vars packages.To perform cointegration and Granger causality tests, I respectively write :
 
sjv <- vardata[, c("upd", "nc", "r", "up", "op", "ur", "expl")]
sjv.vecm <- ca.jo(sjv, type="eigen", K=2, spec = "longrun", season =4)
summary(sjv.vecm)
 
reg1.caus <- VAR(vardata[, c("upd", "nc", "r", "up", "op", "ur", "expl")],
p = 2, type = "const")
causality(reg1.caus, cause = "up")
 
In both cases, I respectively obtain the following error messages:
 
Error is solve.default(M11) : 
  the system is numerically singular : conditionnement de la réciproque = 9.47575e-17

and 
 
Error is solve.default(crossprod(as.matrix(Z))) : 
  the system is numerically singular : conditionnement de la réciproque = 7.87318e-22

 
What do these messages mean ? And how can I resolve this problem? I precise that I use quarterly data and that when I try to directly estimate VAR model using the command below I encounter no problem:
 
reg1 <- VAR(vardata[, c("upd", "nc", "r", "up", "op", "ur", "expl")],
 p = 1, type ="const")
reg1
 
Thank you in advance for answer. 
Axel
 
 
 


      
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