Estimating serial correlation and self-similarity in financial time series—A diversification approach with applications to high frequency data

• Review of self-similarity estimation methods for financial time series.
• Performance test for estimation methods under typical financial market conditions.
• Improved estimation by “diversification of methods” for sake of higher robustness.
• Naïve diversification and minimum variance portfolio approach.
• Application to real market data shows different regimes of serial correlation level.

We derive a heuristic method to estimate the degree of self-similarity and serial correlation in financial time series. Especially, we propagate the use of a tailor-made selection of different estimation techniques that are used in various fields of time series analysis but until now have not consequently found their way into the finance literature. Following the idea of portfolio diversification, we show that considerable improvements with respect to robustness and unbiasedness can be achieved by using a basket of estimation methods.With this methodological toolbox at hand, we investigate real market data to show that noticeable deviations from the assumptions of constant self-similarity and absence of serial correlation occur during certain periods. On the one hand, this may shed a new light on seemingly ambiguous scientific findings concerning serial correlation of financial time series. On the other hand, a proven time-changing degree of self-similarity may help to explain high-volatility clusters of stock price indices.