Long-term stochastic dependence in financial prices: evidence from the German stock market

Abstract

A number of authors have argued that financial prices may exhibit hidden long-term dependence. We consider this claim analysing German stock market data. Applying three different concepts for the identification of long memory effects, virtually no evidence of such behaviour is found for stock market returns. Another recent assertion says that long term memory may not be pertinent to stock returns but rather to the conditional volatility of financial market prices. As it turns out, this claim is very much supported by our investigation of German stock market data. Furthermore, the long memory property is more pronounced in absolute values of returns than in the squares of returns (both used as proxies for volatility). The methods employed are: the time-honoured procedure of estimating the Hurst exponent for the scaling behaviour of the range of cumulative departures from the mean of a time series, the modified range analysis.