Error when attempting to estimate GARCH model in R

Question

Here is the code I'm using to create my time series:

#Violent Crimes Time Series
violent <- crime[,1]
viol.ts <- ts(violent, start=1960, end=2013, frequency=1)
viol.train <- window(viol.ts, start=1960, end=2003)
viol.test <- window(viol.ts, start=2004)
ts.plot(viol.ts, type="l", xlab="Year", ylab="Total Crimes", main="Violent Crime, 1960-2013")

Here is the code I'm using to estimate my GARCH model:

#GARCH
viol.g <- garchFit(~arma(1,1) + garch(1,1), viol.ts)
summary(viol.g)
plot(viol.g)
plot(viol.g@h.t, type="l")
plot (viol.g@fitted, type="l")

I keep getting the error

Error in solve.default(fit$hessian) : system is computationally singular: reciprocal condition number = 3.27071e-20

and have no idea what is going wrong.

Answer 1

system is computationally singular means it is not possible to obtain the inverse of the second derivative of the log likelihood wrt the parameters ( fit$hessian ). MLE estimates parameters that minimize the log likelihood function but, without it, it is not possible to satisfy the second order condition - this is in theory and the actual implementation of the package may be different.

With a random sample, the function works without a problem as shown below and you may check your data.

library(fGarch)

#Violent Crimes Time Series
set.seed(1237)
violent <- sample(log(10:30), 53, replace = TRUE)
viol.ts <- ts(violent, start=1960, end=2013, frequency=1)
viol.train <- window(viol.ts, start=1960, end=2003)
viol.test <- window(viol.ts, start=2004)
ts.plot(viol.ts, type="l", xlab="Year", ylab="Total Crimes", main="Violent Crime, 1960-2013")

#GARCH
viol.g <- garchFit(~arma(1,1) + garch(1,1), viol.ts)
summary(viol.g)
plot(viol.g)
plot(viol.g@h.t, type="l")
plot (viol.g@fitted, type="l")

Title:
  GARCH Modelling 

Call:
  garchFit(formula = ~arma(1, 1) + garch(1, 1), data = viol.ts) 

Mean and Variance Equation:
  data ~ arma(1, 1) + garch(1, 1)
<environment: 0x0000000030109de0>
  [data = viol.ts]

Conditional Distribution:
  norm 

Coefficient(s):
  mu          ar1          ma1        omega       alpha1        beta1  
5.42739444  -0.83160492   0.90173149   0.06406353   0.00000001   0.39089064