loglik.pci: Computes the log likelihood of a partially cointegrated model
In partialCI: Partial Cointegration

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the log likelihood of a partially cointegrated model

loglik.pci(Y, X, beta, rho, sigma_M, sigma_R, 
  M0 = 0, R0 = 0, 
  calc_method = c("css", "kfas", "ss", "sst", "csst"), 
  nu = pci.nu.default())

`Y`	The time series that is to be modeled. A plain or `zoo` vector of length `n`.
`X`	A (possibly `zoo`) matrix of dimensions `n` x `k`. If `k=1`, then this may be a plain or `zoo` vector.
`beta`	A vector of length `k` representing the weightings to be given to the components of `X`.
`rho`	The coefficient of mean reversion.
`sigma_M`	The standard deviation of the innovations of the mean-reverting component of the model.
`sigma_R`	The standard deviation of the innovations of the random walk component of the model.
`M0`	The initial value of the mean-reverting component. Default = 0.
`R0`	The initial value of the random walk component. Default = 0.
`calc_method`	Specifies the Kalman filter implementation that will be used for computing the likelihood score: "ss" Steady-state Kalman filter "css" C++ implementation of steady-state Kalman filter "kfas" Kalman filter implementation of the KFAS package "sst" Steady-state Kalman filter using t-distributed innovations "csst" C++ implementation of steady-state Kalman filter using t-distributed innovations Default: `css`
`nu`	The degrees-of-freedom parameter to be used if `calc_method` is "sst" or "csst".

The partial cointegration model is given by the equations:

Y[t] = beta[1] * X[t,1] + beta[2] * X[t,2] + ... + beta[k] * X[t,k] + M[t] + R[t]

M[t] = rho * M[t-1] + epsilon_M[t]

R[t] = R[t-1] + epsilon_R[t]

-1 < rho < 1

epsilon_M[t] ~ N(0, sigma_M^2)

epsilon_R[t] ~ N(0, sigma_R^2)

Given the input series Y and X, and given the parameter values beta, rho, M0 and R0, the innovations epsilon_M[t] and epsilon_R[t] are calculated using a Kalman filter. Based upon these values, the log-likelihood score is then computed and returned.

The log of the likelihood score of the Kalman filter

Matthew Clegg matthewcleggphd@gmail.com

Christopher Krauss christopher.krauss@fau.de

Jonas Rende jonas.rende@fau.de

Clegg, Matthew, 2015. Modeling Time Series with Both Permanent and Transient Components using the Partially Autoregressive Model. Available at SSRN: http://ssrn.com/abstract=2556957

egcm Engle-Granger cointegration model

partialAR Partially autoregressive models

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

    set.seed(1)
    YX <- rpci(n=500, beta=c(2,3,4), sigma_C=c(1,1,1), rho=0.9, sigma_M=0.1, sigma_R=0.2)
    loglik.pci(YX[,1], YX[,2:ncol(YX)], beta=c(2,3,4), rho=0.9, sigma_M=0.1, sigma_R=0.2)