Robustez em processos heterocedásticos contaminados por outliers aditivos: uma abordagem M-Quantile

Abstract

Financial time series have characteristics that distinguish them from other existing series, commonly known as stylized financial series facts. One of these characteristics is the presence of outliers in the series, which makes its modeling and forecasting difficult. Additionally, these series have substantial sensitivity to political, social and economic decisions, generating an increase in their volatility. This research has the goal to introduce the M quantile regression estimator, discussed in Breckling e Chambers (1988), as alternative approach to estimate the parameters of the Generalized Autoregressive with conditional heterocestatic variance (GARCH) process.It is well-know that the M-regression estimator is strong against additive outliers, that is, it has the robustness property, and it has recently been widely used to estimate linear time series with different correlation structures, either in the time or frequency-domain. Simulation will be carried out to verify the performance of the method for small sample sizes. Time series with time-dependent variance (volatility) have been studied by several authors in different areas of applications. Here, in particular, the motivation of the proposed study in a real-problem is to modelling and forecasting variables from financial data area, with special attention to assets returns variables which, in general, do not preserve the property of constant variance over time.