Browsing by Author "BOUMAILA, Nadia"

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Inference in periodic restricted EXPAR models
    (Université Badji Mokhtar Annaba, 2026) BOUMAILA, Nadia
    This thesis investigates the probabilistic and statistical properties of the periodic restricted exponential autoregressive (PEXPAR) process. By leveraging Markov chain theory, we establish conditions for strict periodic stationarity. Parameter estimation is performed using the quasi-maximum likelihood (QML)method, while model adequacy is assessed through Wald, Likelihood Ratio (LR) and Lagrange Multiplier (LM) tests to evaluate linearity and the nullity of final coefficients. Simulation studies support these findings by demonstrating the accuracy of the proposed tests in maintaining correct nominal levels and increasing power as the sample size grows, thereby validating the practical applicability of the methodology across various scenarios. In addition, we propose a recursive estimation algorithm for the restricted exponential autoregressive (EXPAR) model. This algorithm, based on the matrix inversion lemma, allows for efficient online estimation through Recursive Least Squares (RLS). It is shown that the RLS estimators are asymptotically efficient. A short simulation study highlights the excellent performance of the proposed estimators. Finally, we apply both periodic autoregressive (PAR) and PEXPAR models to precipitation time series data from Algeria, Illustrating the practical relevance of our findings.