kalman

kalman filtering and smoothing for vector autoregression with measurement error

The model is high-dimensional vector autoregression with measurement error, also known as linear gaussian state-space model. Provable sparse expectation-maximization algorithm is provided for the estimation of transition matrix and noise variances. Global and simultaneous testings are implemented for transition matrix with false discovery rate control. For more information, see the accompanying paper: Lyu, X., Kang, J., & Li, L. (2023). "Statistical inference for high-dimensional vector autoregression with measurement error", Statistica Sinica.

Xiang Lyu

hdiVAR

Statistical Inference for Noisy Vector Autoregression

Jian Kang

Lexin Li

kalman function

<dl><dt>Y</dt>
<dd>observations of time series, a p by T matrix.</dd>
<dt>A</dt>
<dd>current estimate of transition matrix.</dd>
<dt>sig_eta</dt>
<dd>current estiamte of \(\sigma_\eta\).</dd>
<dt>sig_epsilon</dt>
<dd>current estiamte \(\sigma_\epsilon\).</dd>
<dt>X_init</dt>
<dd>inital estimate of latent \(x_1\) at the first iteration, a p-dimensional vector.</dd>
<dt>P_init</dt>
<dd>inital covariance estimate of latent \(x_1\) at the first iteration, a p by p matrix.</dd></dl>

Arguments

Author

kalman filtering and smoothing for vector autoregression with measurement error — kalman

<dl>

<dt>Y</dt>
<dd>observations of time series, a p by T matrix.</dd>


<dt>A</dt>
<dd>current estimate of transition matrix.</dd>


<dt>sig_eta</dt>
<dd>current estiamte of \(\sigma_\eta\).</dd>


<dt>sig_epsilon</dt>
<dd>current estiamte \(\sigma_\epsilon\).</dd>


<dt>X_init</dt>
<dd>inital estimate of latent \(x_1\) at the first iteration, a p-dimensional vector.</dd>


<dt>P_init</dt>
<dd>inital covariance estimate of latent \(x_1\) at the first iteration, a p by p matrix.</dd>

</dl>

kalman: kalman filtering and smoothing for vector autoregression with measurement error

Description

Usage

Value

Arguments

Author