M-periodogram for the analysis of long-range-dependent time series.

This paper focuses on time series with long-memory and suggests using an alternative periodogram, called M-periodogram, which is obtained by relating the periodogram to a regression problem and then using an M-estimator for the coefficients of the regression model. The asymptotic properties of this novel M-periodogram are established and its empirical properties are investigated for finite samples under different scenarios. Furthermore, in addition to being an appealing alternative periodogram for long-memory time series, it is also resistant to additive outliers. We investigate the robustness performance of the estimator through simulation. As a practical application, the paper investigates the effect of atypical observations in air pollution data, namely daily Particulate Matter (<inline-graphic></inline-graphic>) observations. Besides the importance of modelling and forecasting this pollutant, the <inline-graphic></inline-graphic> series presents, in general, interesting features such as seasonal poles, asymmetry, and also high levels of pollution which can be regarded as atypical observations in the context of this work. [ABSTRACT FROM AUTHOR]