loglik.par: Negative log likelihood of a partially autoregressive fit

Description

Negative log likelihood of a partially autoregressive fit

Usage

loglik.par(Y, rho, sigma_M, sigma_R, M0 = 0, R0 = Y[1], 
  calc_method = c("css", "fkf", "ss", "sst", "csst"), 
  nu = par.nu.default())

Arguments

A numeric vector representing the time series to which the partially autoregressive model is being fit.

rho

The coefficient of mean reversion

sigma_M

Standard deviation of the innovations of the mean-reverting process

sigma_R

Standard deviation of the innovations of the random walk process

Initial value of the mean-reverting process

Initial value of the random walk process

calc_method

The method to be used for calculating the negative log likelihood.

"ss"Steady-state Kalman filter with normally distributed errors
"css"Steady-state Kalman filter with normally distributed errors, coded in C++

If calc_method is "sst" or "csst", this specifies the number of degrees of freedom of the t-distribution.

Value

Returns the negative log likelihood of fitting the partially autoregressive model with parameters (rho, sigma_M, sigma_R, M0, R0) to the data series Y.

References

Clegg, Matthew. Modeling Time Series with Both Permanent and Transient Components using the Partially Autoregressive Model. Available at SSRN: http://ssrn.com/abstract=2556957

Examples

Run this code

loglik.par(0,0,0,1)  # -> same as -log(dnorm(0))
loglik.par(0,0,1,0)  # -> same as -log(dnorm(0))
loglik.par(0,0,1,1)  # -> same as -log(dnorm(0,0,sqrt(2)))