dlm.lpl {DGM}

Calculate the log predictive likelihood for a specified set of parents and a fixed delta.

Description

Calculate the log predictive likelihood for a specified set of parents and a fixed delta.

Usage

dlm.lpl(Yt, Ft, delta, priors = priors.spec())

Arguments

Yt

the vector of observed time series, length T.

Ft

the matrix of covariates, dim = number of thetas (p) x number of time points (T), usually a row of 1s to represent an intercept and the time series of the parent nodes.

delta

discount factor (scalar).

priors

list with prior hyperparameters.

Value

mt

the vector or matrix of the posterior mean (location parameter), dim = p x T.

Ct

and CSt the posterior scale matrix C_{t} is C_{t} = C*_{t} x S_{t}, with dim = p x p x T, where S_{t} is a point estimate for the observation variance phi^{-1}

Rt

and RSt the prior scale matrix R_{t} is R_{t} = R*_{t} x S_{t-1}, with dim = p x p x T, where S_{t-1} is a point estimate for the observation variance phi^{-1} at the previous time point.

nt

and dt the vectors of the updated hyperparameters for the precision phi with length T.

S

the vector of the point estimate for the observation variance phi^{-1} with length T.

ft

the vector of the one-step forecast location parameter with length T.

Qt

the vector of the one-step forecast scale parameter with length T.

ets

the vector of the standardised forecast residuals with length T, \newline defined as (Y_{t} - f_{t}) / sqrt (Q_{t}).

lpl

the vector of the Log Predictive Likelihood with length T.

References

West, M. & Harrison, J., 1997. Bayesian Forecasting and Dynamic Models. Springer New York.

Examples

data("utestdata")
Yt = myts[,1]
Ft = t(cbind(1,myts[,2:5]))
m = dlm.lpl(Yt, Ft, 0.7)