Analysis of the global financial crisis using statistical moments

- We introduce a method of standardizing stock-market indices.
- We introduce the normalization of the distribution of the standardized data.
- We use IMF quarterly figures from Q1 2000 to Q3 2013 for 54 countries.
- We detect the global financial crisis by the movements of skewness and kurtosis.
- We suggest a possible warning signal of the global financial crisis.

In this paper, we investigate the impacts of the global financial crisis on the statistical properties of the stock market indices. And we also suggest a possible warning signal of the global financial crisis from the changes in the statistical properties. In order to do that, we treat the world stock markets as a web of relations, which is described by a distribution in the standardized normalization coordinate system: Quarterly world stock-market indices are standardized by re-scaling each index and then normalizing the whole time-series so that every sample of standardized indices has the same mean and variance. By plotting the higher moments of this normalized series, it is possible to identify singularities which might have warned of the dotcom bubble crash in 2002, the 2008 financial crisis, and the European sovereign debt crisis of 2009-10.