Statistical Methods in Finance 2016

Abstract

Financial time series analyses: Near extreme events, correlations and comovements

by Anirban Chakrabarti

We would like to present our works on financial time series in two different directions: 1. (Near) extreme event statistics, which plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results in extreme value statistics is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focusing, instead, on the closely related density of "near-extremes" - the distance between a record and the maximal value - can render the statistical methods to be more suitable in the practical applications and/or validations of financial market models. 2. Correlations and co-movements in financial market: The daily return time series from the stock market may be used to compute the correlation matrices and calculate the similarity "distances". The multi-dimensional scaling and minimum spanning tree methods are then used to visualize the dynamic evolution of the stock market. These methods help to differentiate sectors in the market in the form of clusters.

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