.ts_pmm2_fit

Implementation of PMM2 algorithm for time series models with various approaches
depending on the model structure (AR, MA, ARMA, ARIMA)

internal

Implements the Polynomial Maximization Method ('PMM') for parameter estimation
in linear and time series models when error distributions deviate from normality.
The 'PMM2' variant achieves lower variance parameter estimates compared to ordinary
least squares ('OLS') when errors exhibit significant skewness. Includes methods
for linear regression, 'AR'/'MA'/'ARMA'/'ARIMA' models, and bootstrap inference.
Methodology described in Zabolotnii, Warsza, and Tkachenko (2018) <doi:10.1007/978-3-319-77179-3_75>,
Zabolotnii, Tkachenko, and Warsza (2022) <doi:10.1007/978-3-031-03502-9_37>, and
Zabolotnii, Tkachenko, and Warsza (2023) <doi:10.1007/978-3-031-25844-2_21>.

Serhii Zabolotnii

EstemPMM

Polynomial Maximization Method for Non-Gaussian Regression

.ts_pmm2_fit function

<dl><dt>b_init</dt>
<dd>initial parameter estimates (AR followed by MA)</dd>
<dt>innovations_init</dt>
<dd>initial innovations (errors)</dd>
<dt>model_info</dt>
<dd>list with model structure information</dd>
<dt>m2, m3, m4</dt>
<dd>central moments</dd>
<dt>max_iter</dt>
<dd>maximum number of iterations</dd>
<dt>tol</dt>
<dd>convergence tolerance</dd>
<dt>regularize</dt>
<dd>logical, add small value to diagonal for numerical stability</dd>
<dt>reg_lambda</dt>
<dd>regularization parameter (if regularize=TRUE)</dd>
<dt>verbose</dt>
<dd>logical, whether to print progress information</dd></dl>

Arguments

PMM2 fitting algorithm for time series models — .ts_pmm2_fit

<dl>

<dt>b_init</dt>
<dd>initial parameter estimates (AR followed by MA)</dd>


<dt>innovations_init</dt>
<dd>initial innovations (errors)</dd>


<dt>model_info</dt>
<dd>list with model structure information</dd>


<dt>m2, m3, m4</dt>
<dd>central moments</dd>


<dt>max_iter</dt>
<dd>maximum number of iterations</dd>


<dt>tol</dt>
<dd>convergence tolerance</dd>


<dt>regularize</dt>
<dd>logical, add small value to diagonal for numerical stability</dd>


<dt>reg_lambda</dt>
<dd>regularization parameter (if regularize=TRUE)</dd>


<dt>verbose</dt>
<dd>logical, whether to print progress information</dd>

</dl>

.ts_pmm2_fit: PMM2 fitting algorithm for time series models

Description

Usage

Value

Arguments