DELTA() function gives the value of the component of vector DELTA \(\boldsymbol{\Delta}\). See Regui et al. (2024) for periodic simple regression model. \(\mathbf{\Delta}= \left[\begin{array}{c} \mathbf{\Delta}_1 \\ \mathbf{\Delta}_2\\ \mathbf{\Delta}_3 \end{array}\right]\ \), where \( \mathbf{\Delta}_1\) is a vector of dimension \(S\) with component \( \frac{n^{\frac{-1}{2} } }{\widehat{ \sigma}_s}\sum\limits_{\underset{ }{r=0}}^{m-1}\widehat{\phi}(Z_{s+Sr,t})\), \(\mathbf{\Delta}_2\) is a vector of dimension \(pS\) with component \(\frac{ n^{\frac{-1}{2} } }{\widehat{\sigma}_{s}}\sum\limits_{\underset{ }{r=0}}^{m-1} \widehat{\phi}(Z_{s+Sr})K_{s}^{(n)} \mathbf{X}_{s+Sr} \), \(\mathbf{\Delta}_3\) is a vector of dimension \(S\) with component \( \frac{n^{\frac{-1}{2} } }{2\widehat{\sigma}_{s}^{2}}\sum\limits_{\underset{ }{r=0}}^{m-1}{Z_{s+Sr} \widehat{\phi}(Z_{s+Sr})-1 }\).
DELTA(x,phi,s,e,sigma)returns the values of \(\mathbf{\Delta}\). See Regui et al. (2024) for simple periodic coefficients regression model.
A list of independent variables with dimension \(p\).
phi_n.
A period of the regression model.
The residuals vector.
sd_estimation_for_each_s.
Regui, S., Akharif, A., & Mellouk, A. (2024). "Locally optimal tests against periodic linear regression in short panels." Communications in Statistics-Simulation and Computation, 1--15. tools:::Rd_expr_doi("https://doi.org/10.1080/03610918.2024.2314662")