GetL {bcpa} | R Documentation |
Obtain likelihood estimates of gappy Gaussian time series
Description
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. |
Value
Returns the log-likelihood of the data.
Author(s)
Eliezer Gurarie
See Also
Core function of BCPA, used directly in GetRho
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))
[Package bcpa version 1.3.2 Index]