MCMCresidualBreakAnalysis {MCMCpack} | R Documentation |
This function performs a break analysis for univariate time series data using
a linear Gaussian changepoint model. The code is written mainly for an internal
use in testpanelSubjectBreak
.
MCMCresidualBreakAnalysis(resid, m = 1, b0 = 0, B0 = 0.001, c0 = 0.1, d0 = 0.1, a = NULL, b = NULL, mcmc = 1000, burnin = 1000, thin = 1, verbose = 0, seed = NA, beta.start = NA, P.start = NA, marginal.likelihood = c("none", "Chib95"), ...)
resid |
Univariate time series |
m |
The number of breaks. |
b0 |
The prior mean of beta. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the prior mean for all of the betas. |
B0 |
The prior precision of beta. This can either be a scalar or a square matrix with dimensions equal to the number of betas. If this takes a scalar value, then that value times an identity matrix serves as the prior precision of beta. Default value of 0 is equivalent to an improper uniform prior for beta. |
c0 |
c0/2 is the shape parameter for the inverse Gamma prior on sigma^2 (the variance of the disturbances). The amount of information in the inverse Gamma prior is something like that from c0 pseudo-observations. |
d0 |
d0/2 is the scale parameter for the inverse Gamma prior on sigma^2 (the variance of the disturbances). In constructing the inverse Gamma prior, d0 acts like the sum of squared errors from the c0 pseudo-observations. |
a |
a is the shape1 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. |
b |
b is the shape2 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. |
burnin |
The number of burn-in iterations for the sampler. |
mcmc |
The number of MCMC iterations after burnin. |
thin |
The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value. |
verbose |
A switch which determines whether or not the progress of
the sampler is printed to the screen. If |
seed |
The seed for the random number generator. If NA, the Mersenne
Twister generator is used with default seed 12345; if an integer is
passed it is used to seed the Mersenne twister. The user can also
pass a list of length two to use the L'Ecuyer random number generator,
which is suitable for parallel computation. The first element of the
list is the L'Ecuyer seed, which is a vector of length six or NA (if NA
a default seed of |
beta.start |
The starting values for the beta vector. This can either be a scalar or a column vector with dimension equal to the number of betas. The default value of of NA will use the OLS estimate of beta as the starting value. If this is a scalar, that value will serve as the starting value mean for all of the betas. |
P.start |
The starting values for the transition matrix.
A user should provide a square matrix with dimension equal to the number of states.
By default, draws from the |
marginal.likelihood |
How should the marginal likelihood be
calculated? Options are: |
... |
further arguments to be passed |
MCMCresidualBreakAnalysis
simulates from the posterior distribution using
standard Gibbs sampling (a multivariate Normal draw for the betas, and an
inverse Gamma draw for the conditional error variance). The simulation
proper is done in compiled C++ code to maximize efficiency. Please consult
the coda documentation for a comprehensive list of functions that can be
used to analyze the posterior sample.
The model takes the following form:
y_i ~ N(beta_m, sigma^2_m), m = 1,...,M.
We assume standard, semi-conjugate priors:
beta ~ N(b0,B0^(-1))
And:
sigma^(-2) ~ Gamma(c0/2, d0/2)
Where beta and sigma^(-2) are assumed a priori independent.
And:
p_mm ~ Beta(a, b), m = 1,...,M.
Where M is the number of states.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
Jong Hee Park, 2011. “A Unified Method for Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models." Working Paper.
Siddhartha Chib. 1998. “Estimation and comparison of multiple change-point models.” Journal of Econometrics. 86: 221-241.
## Not run: line <- list(X = c(-2,-1,0,1,2), Y = c(1,3,3,3,5)) ols <- lm(Y~X) residual <- rstandard(ols) posterior <- MCMCresidualBreakAnalysis(residual, m = 1, data=line, mcmc=1000, verbose=200) plotState(posterior) summary(posterior) ## End(Not run)