Ensemble vs. time averages in financial time series analysis

Empirical analysis of financial time series suggests that the underlying stochastic dynamics are not only non-stationary, but also exhibit non-stationary increments. However, financial time series are commonly analyzed using the sliding interval technique that assumes stationary increments. We propose an alternative approach that is based on an ensemble over trading days. To determine the effects of time averaging techniques on analysis outcomes, we create an intraday activity model that exhibits periodic variable diffusion dynamics and we assess the model data using both ensemble and time averaging techniques. We find that ensemble averaging techniques detect the underlying dynamics correctly, whereas sliding intervals approaches fail. As many traded assets exhibit characteristic intraday volatility patterns, our work implies that ensemble averages approaches will yield new insight into the study of financial markets’ dynamics. ► Empirical evidence for non-stationary increments in financial time series is provided. ► An ensemble average approach to assess financial time series is proposed. ► Based on empirical analysis, we define an intraday volatility model. ► Using model data, we compare time and ensemble averaging techniques. ► The ensemble average approach identifies the underlying model dynamics correctly.