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

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 sulfur dioxide (SO2) pollutant concentrations which have seasonal long-memory features and occasional large peak pollutant concentrations.

[1]  S. R. C. Lopes,et al.  Correlated Errors in the Parameters Estimation of the ARFIMA Model: A Simulated Study , 2006 .

[2]  Céline Lévy-Leduc,et al.  Modeling and forecasting daily average PM10 concentrations by a seasonal long-memory model with volatility , 2014, Environ. Model. Softw..

[3]  Nazmul Sohel,et al.  Estimation of sulfur dioxide air pollution concentrations with a spatial autoregressive model , 2013 .

[4]  Philip Hans Franses,et al.  Long memory and level shifts: Re-analyzing inflation rates , 1999 .

[5]  Miguel A. Delgado,et al.  Optimal spectral bandwidth for long memory , 1993 .

[6]  Bonnie K. Ray,et al.  ESTIMATION OF THE MEMORY PARAMETER FOR NONSTATIONARY OR NONINVERTIBLE FRACTIONALLY INTEGRATED PROCESSES , 1995 .

[7]  Jan Beran,et al.  On a class of M-estimators for Gaussian long-memory models , 1994 .

[8]  Wai-Sum Chan,et al.  A note on time series model specification in the presence of outliers , 1992 .

[9]  Josu Arteche,et al.  Semiparametric Inference in Seasonal and Cyclical Long Memory Processes , 2000 .

[10]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[11]  R. Leipus,et al.  A generalized fractionally differencing approach in long-memory modeling , 1995 .

[12]  Sílvia R. C. Lopes,et al.  Some simulations and applications of forecasting long-memory time-series models , 1999 .

[13]  M. Genton,et al.  Highly Robust Estimation of the Autocovariance Function , 2000 .

[14]  S. Porter-Hudak.  An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates , 1990 .

[15]  Eric Moulines,et al.  Asymptotic properties of U-processes under long-range dependence , 2009, 0912.4688.

[16]  Céline Lévy-Leduc,et al.  Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes , 2009, 0912.4686.

[17]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[18]  Céline Lévy-Leduc,et al.  An M-estimator for the long-memory parameter , 2017 .

[19]  Ignacio N. Lobato,et al.  Averaged periodogram estimation of long memory , 1996 .

[20]  Céline Lévy-Leduc,et al.  Robust estimation of periodic autoregressive processes in the presence of additive outliers , 2010, J. Multivar. Anal..

[21]  Xunyu Ye,et al.  Improving estimation of the fractionally differencing parameter in the SARFIMA model using tapered periodogram , 2015 .

[22]  P. Rousseeuw,et al.  Alternatives to the Median Absolute Deviation , 1993 .

[23]  Henghsiu Tsai,et al.  Inference of seasonal long-memory aggregate time series , 2012, 1211.5513.

[24]  G. O. L. C. Marques,et al.  Empirical aspects of the Whittle-based maximum likelihood method in jointly estimating seasonal and , 2011 .

[25]  Josu Arteche,et al.  Semiparametric robust tests on seasonal or cyclical long memory time series , 2002 .

[26]  Kin-che Lam,et al.  Synoptic typing and its application to the assessment of climatic impact on concentrations of sulfur dioxide and nitrogen oxides in Hong Kong , 2000 .

[27]  B. Ray.  Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model , 1993 .

[28]  Nan-Jung Hsu,et al.  Semiparametric estimation for seasonal long-memory time series using generalized exponential models , 2009 .

[29]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[30]  Ruei-Hao Shie,et al.  The influence of emission sources and meteorological conditions on SO2 pollution in Mongolia , 2012 .

[31]  P. Rousseeuw,et al.  Explicit scale estimators with high breakdown point , 1992 .

[32]  Wilfredo Palma,et al.  Estimating seasonal long-memory processes: a Monte Carlo study , 2006 .

[33]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[34]  Bengt G. Martinsson,et al.  Composition and evolution of volcanic aerosol from eruptions of Kasatochi, Sarychev and Eyjafjallajökull in 2008-2010 based on CARIBIC observations , 2012 .

[35]  Francisco Cribari-Neto,et al.  Robust estimation in long-memory processes under additive outliers , 2009 .

[36]  V. Reisen,et al.  ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA(p, d, q) MODEL USING THE SMOOTHED PERIODOGRAM , 1994 .

[37]  J. R. M. Hosking,et al.  FRACTIONAL DIFFERENCING MODELING IN HYDROLOGY , 1985 .

[38]  Henghsiu Tsai,et al.  Inference of Seasonal Long‐memory Time Series with Measurement Error , 2015 .

[39]  C. Velasco,et al.  NON-GAUSSIAN LOG-PERIODOGRAM REGRESSION , 2000, Econometric Theory.

[40]  Uwe Hassler,et al.  MIS)SPECIFICATION OF LONG MEMORY IN SEASONAL TIME SERIES , 1994 .

[41]  W. Palma.  Long-Memory Time Series: Theory and Methods , 2007 .

[42]  Sílvia R. C. Lopes,et al.  Invariance of the first difference in ARFIMA models , 2006, Comput. Stat..

[43]  Arslan Saral,et al.  Prediction of Ground Level SO2 Concentration using Artificial Neural Networks , 2003 .

[44]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[45]  Pilar Loreto Iglesias,et al.  Data analysis using regression models with missing observations and long-memory: an application study , 2006, Comput. Stat. Data Anal..

[46]  M. Otto,et al.  Outliers in Time Series , 1972 .

[47]  Eric Moulines,et al.  Large sample behaviour of some well-known robust estimators under long-range dependence , 2011 .

[48]  Wilfredo Palma,et al.  Efficient Estimation of Seasonal Long‐Range‐Dependent Processes , 2005 .

[49]  Wai-Sum Chan,et al.  Outliers and financial time series modelling: a cautionary note , 1995 .

[50]  Jussi Tolvi.  Long memory and outliers in stock market returns , 2003 .

[51]  S. Vitabile,et al.  Two-days ahead prediction of daily maximum concentrations of SO2, O3, PM10, NO2, CO in the urban area of Palermo, Italy , 2007 .

[52]  Wilfredo Palma,et al.  A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model , 2014, Math. Comput. Simul..

[53]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[54]  Wilfredo Palma,et al.  Estimation of seasonal fractionally integrated processes , 2006, Comput. Stat. Data Anal..