# [R-SIG-Finance] Spread Libor-Fed Fund Rate: ARIMA(1,1,1)

Andreas Klein klein82517 at yahoo.de
Tue Feb 10 14:25:11 CET 2009

```Hello.

I have 246 realizations of the spread of the 3 Month Libor (L3M) and the Fed Fund Rate (FFR) from January 1985 to June 2005. I took the logarithms of L3M and FFR and calculated the difference. At last I obtain my 246 observations.

With the SBC or BIC criterion I identified an ARIMA(1,1,1)-process.
The estimation gives the folllowing results:

> x <- log(L3M)-log(FFR)
> arima(x,order=c(1,1,1),method="ML",include.mean=FALSE)

Call:
arima(x = x, order = c(1, 1, 1), include.mean = FALSE, method = "ML")

Coefficients:
ar1      ma1
0.6890  -0.9185
s.e.  0.1374   0.0917

sigma^2 estimated as 0.002002:  log likelihood = 413.25,  aic = -820.5

Now I try the model based bootstrap to test for significance of the coefficients:

model <- arima(x,order=c(1,1,1),method="ML",include.mean=FALSE)

ar1 <- as.numeric(model\$coef[1])
ma1 <- as.numeric(model\$coef[2])

res <- model\$res[3:246]-mean(model\$res[3:246])

ar1_boot <- numeric(10000)
ma1_boot <- numeric(10000)

for (i in 1:10000) {

res_boot <- sample(res,replace=TRUE)

bootseries <- numeric(243)

for (t in 4:246) {

bootseries[t-3] <- (1+ar1)*ifelse(t<=4,x[t-1],bootseries[t-4])-ar1*ifelse(t<=5,x[t-2],bootseries[t-5])+res_boot[t-2]+ma1*res_boot[t-3]

}

model_boot <- arima(bootseries,order=c(1,1,1),method="ML",include.mean=FALSE)

ar1_boot[i] <- as.numeric(model_boot\$coef[1])
ma1_boot[i] <- as.numeric(model_boot\$coef[2])

}

When I try to run the code, R interrupts with the following message:
Failure in solve.default(res\$hessian * n.used) :
Lapackroutine dgesv: System is singular

What is wrong???

Regards,
Andreas.

```