t_sampleLogVols

Compute one draw of the log-volatilities using a discrete mixture of Gaussians
approximation to the likelihood (see Omori, Chib, Shephard, and Nakajima, 2007)
where the log-vols are assumed to follow an TAR(1) model with time-dependent
innovation variances. More generally, the code operates for <code>p</code> independent
TAR(1) log-vol processes to produce an efficient joint sampler in <code>O(Tp)</code> time.

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_sampleLogVols function

<dl><dt>h_y</dt>
<dd>the <code>T </code> vector of data, which follow independent SV models</dd>
<dt>h_prev</dt>
<dd>the <code>T</code> vector of the previous log-vols</dd>
<dt>h_mu</dt>
<dd>the <code>1</code> vector of log-vol unconditional means</dd>
<dt>h_phi</dt>
<dd>the <code>1</code> vector of log-vol AR(1) coefficients</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_sigma_eta_0</dt>
<dd>the <code>1</code> vector of initial 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>loc</dt>
<dd>list of the row and column indices to fill in the band-sparse matrix in the sampler</dd></dl>

Arguments

Sample the latent log-volatilities — t_sampleLogVols

<dl>

<dt>h_y</dt>
<dd>the <code>T </code> vector of data, which follow independent SV models</dd>


<dt>h_prev</dt>
<dd>the <code>T</code> vector of the previous log-vols</dd>


<dt>h_mu</dt>
<dd>the <code>1</code> vector of log-vol unconditional means</dd>


<dt>h_phi</dt>
<dd>the <code>1</code> vector of log-vol AR(1) coefficients</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_sigma_eta_0</dt>
<dd>the <code>1</code> vector of initial 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>loc</dt>
<dd>list of the row and column indices to fill in the band-sparse matrix in the sampler</dd>

</dl>

t_sampleLogVols: Sample the latent log-volatilities

Description

Usage

Value

Arguments