t_sampleAR1

Compute one draw of the TAR(1) coefficients in a model with Gaussian innovations
and time-dependent innovation variances. In particular, we use the sampler for the
log-volatility TAR(1) process with the parameter-expanded Polya-Gamma sampler. The sampler also applies
to a multivariate case with independent components.

Provides efficient Markov chain Monte Carlo (MCMC) algorithms for
dynamic shrinkage processes, which extend global-local shrinkage priors to
the time series setting by allowing shrinkage to depend on its own past.
These priors yield locally adaptive estimates, useful for time series and
regression functions with irregular features. The package includes full MCMC
implementations for trend filtering using dynamic shrinkage on signal differences,
producing locally constant or linear fits with adaptive credible bands.
Also included are models with static shrinkage and normal-inverse-Gamma priors for comparison.
Additional tools cover dynamic regression with time-varying coefficients and
B-spline models with shrinkage on basis differences, allowing for flexible
curve-fitting with unequally spaced data. Some support for heteroscedastic errors,
outlier detection, and change point estimation.
Methods in this package are described in Kowal et al. (2019) <doi:10.1111/rssb.12325>,
Wu et al. (2024) <doi:10.1080/07350015.2024.2362269>, Schafer and Matteson (2024)
<doi:10.1080/00401706.2024.2407316>, and Cho and Matteson (2024) <doi:10.48550/arXiv.2408.11315>.

Toryn Schafer

Dynamic Shrinkage Process and Change Point Detection

Daniel R. Kowal

Haoxuan Wu

Jason B. Cho

David S. Matteson

t_sampleAR1 function

<dl><dt>h_yc</dt>
<dd>the <code>T</code> vector of centered log-volatilities
(i.e., the log-vols minus the unconditional means <code>dhs_mean</code>)</dd>
<dt>h_phi</dt>
<dd>the <code>1</code> vector of previous AR(1) coefficient(s)</dd>
<dt>h_phi2</dt>
<dd>the <code>1</code> vector of previous penalty coefficient(s)</dd>
<dt>h_sigma_eta_t</dt>
<dd>the <code>T</code> vector of log-vol innovation standard deviations</dd>
<dt>h_st</dt>
<dd>the <code>T</code> vector of indicators on whether each time-step exceed the estimated threshold</dd>
<dt>prior_dhs_phi</dt>
<dd>the parameters of the prior for the log-volatility AR(1) coefficient <code>dhs_phi</code>;
either <code>NULL</code> for uniform on [-1,1] or a 2-dimensional vector of (shape1, shape2) for a Beta prior
on <code>[(dhs_phi + 1)/2]</code></dd></dl>

Arguments

Sample the TAR(1) coefficients — t_sampleAR1

<dl>

<dt>h_yc</dt>
<dd>the <code>T</code> vector of centered log-volatilities
(i.e., the log-vols minus the unconditional means <code>dhs_mean</code>)</dd>


<dt>h_phi</dt>
<dd>the <code>1</code> vector of previous AR(1) coefficient(s)</dd>


<dt>h_phi2</dt>
<dd>the <code>1</code> vector of previous penalty coefficient(s)</dd>


<dt>h_sigma_eta_t</dt>
<dd>the <code>T</code> vector of log-vol innovation standard deviations</dd>


<dt>h_st</dt>
<dd>the <code>T</code> vector of indicators on whether each time-step exceed the estimated threshold</dd>


<dt>prior_dhs_phi</dt>
<dd>the parameters of the prior for the log-volatility AR(1) coefficient <code>dhs_phi</code>;
either <code>NULL</code> for uniform on [-1,1] or a 2-dimensional vector of (shape1, shape2) for a Beta prior
on <code>[(dhs_phi + 1)/2]</code></dd>

</dl>

t_sampleAR1: Sample the TAR(1) coefficients

Description

Usage

Value

Arguments