Outlier Detection in Functional Time Series

12/18/2019

In recent years methods for representing data through functions or curves have gained attention. Such data are known as functional data. Typical data sets consist of time series and cross-sectional data, such as time series of stock prices. However, the presence of outliers has adverse effects on the modelling and forecasting of functional data. In this context, outliers detection is not an easy task since the whole set of functional data (curves, images or functions) is not always possible to visualise. Nevertheless, procedures for detecting functional outliers have been proposed over recent years. Some of these procedures are based on Functional Principal Components Analysis (FPCA), which assumes each sample curve is drawn from an independent and identical distribution (i.i.d.). This assumption is inconsistent with financial data, where samples are often interlinked by an underlying temporal dynamic process. These dynamics should be taken into account to detect outliers in functional time series. To overcome this situation, a dynamic extension of FPCA that takes into account the dependence structure of the functional data has been proposed. Taking this into consideration, this work introduces an outlier detection method for functional time series based on these dynamic principal components. This technique is applied to anomaly detection in financial data.

Authors in the community:

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  C

  Catarina Padrela Loureiro

  ist180868

Supervisors of this institution:

• 

  I

  Isabel Maria Alves Rodrigues

  ist13196

mathematics - Mathematics

por - Portuguese

Instituto Superior Técnico