CODEWITHSUNDEEP
r
Rishi123
Rishi123

Reputation: 31

Error in maximum likelihood estimation of multivariate t distribution. Please advise

I am trying to fit a multivariate t distribution to CRSPday data in R. But optimization fails with non-finite finite-difference value [11] error every time. Can someone please suggest what am i doing wrong.

Basically i am passing mean, variance/correlation and DF as parameters and optimizing it.

I tried few hacks: changing bounds etc, using BFGS but nothing is working

Code Snippet:

mtfit <- function(series){

  loglik <- function(par) {

   mean <- par[1:4]
   rho12 <- par[5]; rho13 <- par[6]; rho14 <- par[7]
   rho23 <- par[8]; rho24 <- par[9]; rho34 <- par[10]
   var1 <- par[11]; var2 <- par[12]; var3 <- par[13]; var4 <- par[14]
   nu <- par[15]

   cov12 <- rho12*sqrt(var1*var2); cov13 <- rho13*sqrt(var1*var3); cov14 <- 
   rho14*sqrt(var1*var4)
   cov23 <- rho23*sqrt(var2*var3); cov24 <- rho24*sqrt(var2*var4); cov34 <- 
   rho34*sqrt(var3*var4)

   covar <-matrix(c(var1,cov12,cov13,cov14,cov12,var2,cov23,cov24,cov13,cov23,var3,cov34,
                  cov14,cov24,cov34,var4),4,4)

f <- -sum(log(dmvt(x=series, delta=mean, sigma=covar, df=nu, log=FALSE)))
f
 }

 cov1 <- c(1e-2,1e-2,1e-2,1e-2,1e-2,1e-2,1e-10,1e-10,1e-10,1e-10)

 cov2 <- c(0.99,0.99,0.99,0.99,0.99,0.99,1e-3,1e-3,1e-3,1e-3)

 lower <- append(append(c(-1,-1,-1,-1),cov1),2.1)
 upper <- append(append(c(0.01,0.001,0.001,0.001),cov2),7)

 start <- lower

 results <- optim(start, loglik, method = "L-BFGS- 
 B",lower=lower,upper=upper,hessian=T)
 return(results)
 }

 fit_mine <- mtfit(CRSPday[,c(4:7)])

Upvotes: 2

Views: 131

Answers (1)

Rishi123
Rishi123

Reputation: 31

Found a solution to this, hence sharing. Basically use cholesky decomposition instead of correlation to represent the co-variance matrix. In this case the bounds don't cause gradient error. 

 mtfit <- function(series){

  loglik <- function(par) {

   mean <- par[1:4]
   A <- 
  matrix(c(par[5],par[6],par[7],par[8],0,par[9],par[10],par[11],0,0,par[12],
              par[13],0,0,0,par[14]),nrow=4,byrow=T)
   covar <- t(A)%*%A

   f <- -sum(log(dmvt(x=series, delta=mean, sigma=covar, df=nu, log=FALSE)))
   f
 }

  A <- chol(cov(series))

    cov1 <- c(-.1,-.1,-.1,-.1,-.1,-.1,-.1,-.1,-.1,-.1)
   cov2 <- c(.1,.1,.1,.1,.1,.1,.1,.1,.1,.1)

  lower <- append(append(c(-0.02,-0.02,-0.02,-0.02),cov1),2.1)
  upper <- append(append(c(0.02,0.02,0.02,0.02),cov2),15)

   start <- 
     as.vector(c(apply(series,2,mean),A[1,1],A[1,2],A[1,3],A[1,4],A[2,2],
                   A[2,3],A[2,4],A[3,3],A[3,4],A[4,4],4))

  results <- optim(start, loglik, method = "L-BFGS-B",lower=lower, 
        upper=upper,hessian=T)
        return(results)
  }
  fit_mine <- mtfit(CRSPday[,c(4:7)])

Upvotes: 1

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