tvar: MCMC Sampler for Time-Varying Autoregression

In drkowal/dsp: Dynamic Shrinkage Processes

MCMC Sampler for Time-Varying Autoregression

Description

Run the MCMC for a time-varying autoregression with a penalty on first (D=1) or second (D=2) differences of each dynamic autoregressive coefficient. The penalty is determined by the prior on the evolution errors, which include:

• the dynamic horseshoe prior ('DHS');

• the static horseshoe prior ('HS');

• the Bayesian lasso ('BL');

• the normal stochastic volatility model ('SV');

• the normal-inverse-gamma prior ('NIG').

In each case, the evolution error is a scale mixture of Gaussians. Sampling is accomplished with a (parameter-expanded) Gibbs sampler, mostly relying on a dynamic linear model representation.

Usage

tvar(
  y,
  p_max = 1,
  include_intercept = FALSE,
  evol_error = "DHS",
  D = 2,
  useObsSV = FALSE,
  nsave = 1000,
  nburn = 1000,
  nskip = 4,
  mcmc_params = list("mu", "yhat", "beta", "evol_sigma_t2", "obs_sigma_t2", "dhs_phi",
    "dhs_mean"),
  computeDIC = TRUE,
  verbose = TRUE
)

Arguments

y	the T x 1 vector of time series observations
p_max	the maximum order of lag to include
include_intercept	logical; if TRUE, include a time-varying intercept
evol_error	the evolution error distribution; must be one of 'DHS' (dynamic horseshoe prior), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
D	degree of differencing (D = 1 or D = 2)
useObsSV	logical; if TRUE, include a (normal) stochastic volatility model for the observation error variance
nsave	number of MCMC iterations to record
nburn	number of MCMC iterations to discard (burin-in)
nskip	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
mcmc_params	named list of parameters for which we store the MCMC output; must be one or more of: "mu" (conditional mean) "yhat" (posterior predictive distribution) "beta" (dynamic regression coefficients) "evol_sigma_t2" (evolution error variance) "obs_sigma_t2" (observation error variance) "dhs_phi" (DHS AR(1) coefficient) "dhs_mean" (DHS AR(1) unconditional mean)
computeDIC	logical; if TRUE, compute the deviance information criterion DIC and the effective number of parameters p_d
verbose	logical; should R report extra information on progress?

Value

A named list of the nsave MCMC samples for the parameters named in mcmc_params

Note

The data y may NOT contain NAs. The data y will be used to construct the predictor matrix (of lagged values), which is not permitted to include NAs.

Examples

## Not run: 
# Example 1:
simdata = simUnivariate(signalName = "doppler", T = 128, RSNR = 7, include_plot = TRUE)
y = simdata$y

# Note: in general should subtract off the sample mean
p = 6 # Lag
out = tvar(y, p_max = p, include_intercept = FALSE,
                   evol_error = 'DHS', D = 1,
                   mcmc_params = list('mu', 'yhat', 'beta', 'obs_sigma_t2'))

for(j in 1:p)
  plot_fitted(rep(0, length(y) - p),
           mu = colMeans(out$beta[,,j]),
           postY = out$beta[,,j])

plot_fitted(y[-(1:p)],
           mu = colMeans(out$mu),
           postY = out$yhat,
           y_true = simdata$y_true[-(1:p)])

spec_TF = post_spec_dsp(post_ar_coefs = out$beta,
                   post_sigma_e = sqrt(out$obs_sigma_t2[,1]),
                   n.freq = 100)

image(x = 1:(length(y)-p), y = spec_TF$freq, colMeans(log(spec_TF$post_spec)),
     xlab = 'Time', ylab = 'Freqency', main = 'Posterior Mean of Log-Spectrum')

## End(Not run)

drkowal/dsp documentation built on July 19, 2023, 11:42 a.m.