Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations

Abstract

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

Minimax prediction of sequences with periodically stationary increments

“…The value of the mean square error of the optimal estimate is calculated by the formula (32). In the case, when the spectral density f (λ) admits the canonical factorization (22), the spectral characteristic and the value of the mean square error of the optimal estimate ζ(M) can be calculated by the formulas (33), (34).…”

“…For example, V.A. Reisen et al [34] proposed a semiparametric robust estimator for the fractional parameters in the SARFIMA model and illustrated its application to forecasting of sulfur dioxide SO 2 pollutant concentrations. C.C.…”

Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments

“…Methods of parameters estimations and filtering usually do not take into account the issues arising from real data, namely, the presence of outliers, measurement errors, incomplete information about the spectral, or model, structure etc. From this point of view, we see an increasing interest to robust methods of estimation that are reasonable in such cases (see Reisen, et al [45], Solci at al. [47] for the examples of robust estimates of SARIMA and PAR models).…”

Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments

“…From this point of view, we see an increasing interest to robust methods of estimation that are reasonable in such cases. For example, Reisen, et al [45] proposed a semiparametric robust estimator for fractional parameters in the SARFIMA model and illustrated its application to forecast of sulfur dioxide SO 2 pollutant concentrations. Solci at al.…”