Periodically Autoregression Processes and Some of Its Aspects
Diab Ibraheem Diab Al-Awar;
Abstract
In this study we have presented a survey on one of the most important topics in identi cation
of PARMA models. An explicit expression for the asymptotic variance of the sample process
PeACF is modi ed to be used in establishing its bands for the PMA process over the cut-o
region and we have studied the theoretical side therefore we have some applications on it
where the simulation results agree well with the theoretical results.
We found explicit expressions for the generalized eigenvectors of the inverse of invertible
standard multi-companion matrices such that each generalized eigenvector depends on the
corresponding eigenvalue. We discussed some properties such the other matrices, as the
factorization of matrices.
Moreover, we obtained a parametrization of the inverse of invertible standard multicompanion
matrix through the eigenvalues and these additional quantities. The number
of parameters in this parametrization is equal to the number of non-trivial elements of the
inverse of invertible standard multi-companion matrix. The results can be applied to statistical
estimation, simulation and theoretical studies of periodically correlated and multivariate
time series in both discrete- and continuous-time series.
We gave a method for generation of periodically correlated and multivariate ARMA
models whose dynamic characteristics are partially or fully speci ed in terms of spectral
poles and zeroes or their equivalents in the form of eigen-(values/vectors) of associated
model matrices by the inverse of invertible standard multi-companion when the information
93
of the standard multi-companion matrices is not enough for the extracting of the parameters
of the model, and we compared the gotten results from a real data with the last papers
reached, and we found that our technique is better and consistent.
94
of PARMA models. An explicit expression for the asymptotic variance of the sample process
PeACF is modi ed to be used in establishing its bands for the PMA process over the cut-o
region and we have studied the theoretical side therefore we have some applications on it
where the simulation results agree well with the theoretical results.
We found explicit expressions for the generalized eigenvectors of the inverse of invertible
standard multi-companion matrices such that each generalized eigenvector depends on the
corresponding eigenvalue. We discussed some properties such the other matrices, as the
factorization of matrices.
Moreover, we obtained a parametrization of the inverse of invertible standard multicompanion
matrix through the eigenvalues and these additional quantities. The number
of parameters in this parametrization is equal to the number of non-trivial elements of the
inverse of invertible standard multi-companion matrix. The results can be applied to statistical
estimation, simulation and theoretical studies of periodically correlated and multivariate
time series in both discrete- and continuous-time series.
We gave a method for generation of periodically correlated and multivariate ARMA
models whose dynamic characteristics are partially or fully speci ed in terms of spectral
poles and zeroes or their equivalents in the form of eigen-(values/vectors) of associated
model matrices by the inverse of invertible standard multi-companion when the information
93
of the standard multi-companion matrices is not enough for the extracting of the parameters
of the model, and we compared the gotten results from a real data with the last papers
reached, and we found that our technique is better and consistent.
94
Other data
| Title | Periodically Autoregression Processes and Some of Its Aspects | Other Titles | عمليات الارتباط الذاتي الدوري المرتبط وبعض تطبيقاتها | Authors | Diab Ibraheem Diab Al-Awar | Issue Date | 2016 |
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