This paper deals with the estimation of seasonal long-memory time series models in the presence of 'outliers'. It is long known that the presence of outliers can lead to undesirable effects on the statistical estimation methods, for example, substantially impacting the sample autocorrelations. Thus, the aim of this work is to propose a semiparametric robust estimator for the fractional parameters in the seasonal autoregressive fractionally integrated moving average (SARFIMA) model, through the use of a robust periodogram at both very low and seasonal frequencies. The model and some theories related to the estimation method are discussed. It is shown by simulations that the robust methodology behaves like the classical one to estimate the long-memory parameters if there are no outliers (no contamination). On the other hand, in the contaminated scenario (presence of outliers), the standard methodology leads to misleading results while the proposed method is unaffected. The methodology is applied to model and forecast
This paper considers the factor modelling for high-dimensional time series contaminated by additive outliers. We propose a robust variant of the estimation method given in Lam and Yao [12]. The estimator of the number of factors is obtained by an eigenanalysis of a robust non-negative definite covariance matrix. Asymptotic properties of the robust eigenvalues are derived and we show that the resulting estimators have the same convergence rates as those found for the standard eigenvalues estimators. Simulations are carried out to analyse the finite sample size performance of the robust estimator of the number of factors under the scenarios of multivariate time series with and without additive outliers. In the application, the robust factor analysis is performed to reduce the dimensionality of the data and, therefore, to identify the pollution behaviour of the pollutant PM 10 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.