Detection and estimation of structural changes and outliers in unobserved components (Q1979107)

The author considers an additive trend decomposition model \(y_t=\mu_t+s_t+\varepsilon_t\) where \(\mu_t\) is a trend, \(s_t\) is a seasonal and \(\varepsilon_t\) is an irregular component of the time series \(y_t\). Both \(\mu_t\) and \(s_t\) are supposed to be generated by some ARMA model. The paper is devoted to the detection of outliers (considered as very large \(\varepsilon_t\)) and structural changes (long-term changes of ARMA parameters). The author proposes an algorithm of detection based on maximum likelihood estimation of parameters and detection of changes by maxima of sum-of-residual-squares statistics. He proposes to use the Kalman filter for ML evaluation. Results of simulation studies and real data examples are presented.