Statistical analysis by wavelet leaders reveals differences in multi-fractal characteristics of stock price and return series in Turkish high frequency data

The price and return time series are two distinct features of any financial asset. Hence, exam-ining the evolution of multiscale characteristics of price and returns sequential data in timedomain would be helpful in gaining a better understanding of the dynamical evolution mecha-nism of the financial asset as a complex system. In fact, this is important to understand theirrespective dynamics and to design their appropriate predictive models. The main purpose ofthe current work is to investigate the multiscale fractals of price and return high frequency datain Turkish stock market. In this regard, the wavelet leaders computational method is appliedto each high frequency data to reveal its multi-fractal behavior. In particular, the method isapplied to a large set of Turkish stocks and statistical results are performed to check for (i)presence of multi-fractals in price and returnseries and (ii) differences between prices andreturns in terms of multi-fractals. Our statistical results show strong evidence that high fre-quency price and return data exhibit multi-fractal dynamics. In addition, they show evidenceof distinct fractal characteristics on different scales between price and return series. Further-more, our statistical results show evidence of differences in local fluctuation characteristics ofprice and return time series. Therefore, differences in local characteristics are useful to buildspecific predictive models for each type of data for better modeling and prediction to generateprofits. Besides, we found evidence that both long-range correlations and fat-tail distributionscontribute to the multifractality in Turkish stocks. This finding can be attributed to the majorrole played by international investors in increasing the volatility of Turkish stocks.