Temos o prazer de convidar a todos para mais um seminário do Programa de Pós-Graduação em Estatística da UFRGS (PPGEst-UFRGS).
Título: M-robust approach to estimate Seasonal INAR processes and outlier detection based on Wavelets and the application to the daily air
quality index data for the pollutant Carbon.
Resumo: This study investigates the detection of outliers in INAR(1)s models using an approach based on wavelet transforms and robust parameter estimation. Initially, the fundamental concepts of the INAR(1)s model are reviewed, followed by the proposal of a new detection method that combines the Discrete Wavelet Transform (DWT) and the Maximal Overlap Discrete Wavelet Transform (MODWT) with a robust version of conditional least squares (CLS) based on M-estimators. The Seasonal Discrete Wavelet Transform (SDWT) is introduced as an extension of the DWT, adapted to handle seasonality in count time series. The proposed method uses thresholds based on the empirical distribution of the
detail coefficients, enhancing the identification of outlier values. The effectiveness of the procedure was
evaluated through Monte Carlo simulations, comparing the percentage of correctly detected outliers. The practical application, exemplified by air quality index data, demonstrates the relevance and applicability of the method, offering a robust and efficient approach for outlier detection in seasonal daily air
quality index data for the pollutant Carbon.
Keywords: Outliers, Robustness, Wavelets, Thresholds, Time Series, INAR(1)s.