Maximum Likelihood Estimation by hand for normal distribution in R

Question

I am a newbie in R and searched in several forums but didn't got an answer so far. We are asked to do a maximum likelihood estimation in R for an AR(1) model without using the arima() command. We should estimate the intercept alpha, the coefficient beta and the variance sigma2. The data should be following a normal distribution, where I derived the log-likelihood function from. I was then trying to program the function with the following code:

Y <- data$V2
nlogL <- function(theta,Y){
  alpha <- theta[1]
  rho <- theta[2]
  sigma2 <- theta[3]
  logl <- -(100/2)*log(2*pi) - (100/2)*log(theta[3]) - (0.5*theta[3])*sum(Y-(theta[1]/(1-theta[2]))**2)


  return(-logl)
}
par0 <- c(0.1,0.1,0.1)
opt <- optim(par0, nlogL, hessian = TRUE)

When running this code I always get the error message: Error in Y - (theta[1]/(1 - theta[2]))^2 : 'Y' is missing. It would be great if you could have a look whether the likelihood function is derived correctly.

Thank you very much in advance for your help!

hint: you can look more closely at the arguments of the objective function in the examples provided in the ?optim documentation — chinsoon12

homer homer · Accepted Answer · 2016-07-20T17:19:13

Your nlogL function should only take a single argument, theta. So you can fix your immediate problem simply by removing the 2nd argument to the function, and the Y variable would be resolved by its definition outside of nlogL. Alternatively, you could keep the signature of nlogL as-is and pass Y as an additional argument through optim like this: optim(par0, nlogL, hessian = TRUE, Y=Y). Also I would second chinsoon12's suggestion to review ?optim.

Maximum Likelihood Estimation by hand for normal distribution in R

1 Answers