GetL function

Obtain likelihood estimates of gappy Gaussian time series

Obtain likelihood of gappy standardized Gaussian time series "x" sampled at times "t" given parameter "rho" (autocorrelation). Alternatively computes the characteristic time scale "tau".

Arguments

• x: Time series
• t: Sampling times
• rho: Auto-correlation
• tau: logical: Whether or not to compute characteristic time scale instead of rho.

Returns

Returns the log-likelihood of the data.

Examples

# simulate autocorrelated time series
  rho.true <- 0.8
  x.full <- arima.sim(1000, model=list(ar = rho.true))
  t.full <- 1:1000
  
# subsample time series
  keep <- sort(sample(1:1000, 200))
  x <- x.full[keep]
  t <- t.full[keep]
  plot(t,x, type="l")
  
# Obtain MLE of rho
  rhos <- seq(0,.99,.01)
  L <- sapply(rhos, function(r) GetL(x, t, r))
  rho.hat <- rhos[which.max(L)]
  plot(rhos, L, type = "l")
  abline(v = c(rho.true, rho.hat), lty=3:2, lwd=2)
  legend("bottomleft", legend=c("true value","MLE"), lty=3:2, lwd=2, 
         title = expression(rho))
         
# Why tau is better
  tau.true <- -1/log(rho.true)
  taus <- seq(1,10,.1)
  L <- sapply(taus, function(r) GetL(x, t, r, tau = TRUE))
  tau.hat <- taus[which.max(L)]

  plot(taus, L, type = "l")
  abline(v = c(tau.true, tau.hat), lty=3:2, lwd=2)
  legend("bottomleft", legend=c("true value","MLE"), lty=3:2, lwd=2, 
         title = expression(tau))

See Also

Core function of BCPA, used directly in GetRho

Author(s)

Eliezer Gurarie