Constructs a <code>time_series_model</code> for a stationary AR(1) process with parameter
<code>phi</code> and innovation variance <code>sigma2</code>.
The model is
\(X_t = \phi X_{t-1} + \varepsilon_t, \; \varepsilon_t \stackrel{\text{i.i.d.}}{\sim} N(0, \sigma^2)\).
The autocovariance is
\(
\gamma(h) = \mathrm{cov}(X_t, X_{t+h})
= \frac{\sigma^2}{1 - \phi^2}\,\phi^{\lvert h \rvert}
\).

Implements the Generalized Method of Wavelet Moments with Exogenous Inputs estimator (GMWMX) presented in Voirol, L., Xu, H., Zhang, Y., Insolia, L., Molinari, R. and Guerrier, S. (2024) <doi:10.48550/arXiv.2409.05160>.
The GMWMX estimator allows to estimate functional and stochastic parameters of linear models with correlated residuals in presence of missing data.
The 'gmwmx2' package provides functions to load and plot Global Navigation Satellite System (GNSS) data from the Nevada Geodetic Laboratory and functions to estimate linear model model with correlated residuals in presence of missing data.

Lionel Voirol

gmwmx2

Estimate Functional and Stochastic Parameters of Linear Models
with Correlated Residuals and Missing Data

Haotian Xu

Yuming Zhang

Luca Insolia

Roberto Molinari

Stéphane Guerrier

ar1 function

<dl><dt>phi</dt>
<dd>AR(1) coefficient in (-1, 1).</dd>
<dt>sigma2</dt>
<dd>Innovation variance (&gt; 0).</dd></dl>

Arguments

AR(1) process (time_series_model) — ar1

<dl>

<dt>phi</dt>
<dd>AR(1) coefficient in (-1, 1).</dd>


<dt>sigma2</dt>
<dd>Innovation variance (&gt; 0).</dd>

</dl>

ar1: AR(1) process (`time_series_model`)

Description

Usage

Value

Arguments

Examples