Soft Matter and Complex Systems Seminar

Intra-day changes of the activity on stock market is a well-knownempirical fact observed all around the world on different types of market.This specific pattern of activity is often called the lunch effect.Observed seasonality suggest non-stationarity of high frequency financialtime series. However, estimators of the stationary processes are commonlyused (e.g. autocorrelation function estimator). Our aim is to analyticallydescribe this seasonality and use it to transform the time series in sucha way to make it stationary. We present exact formula connecting estimatorof the autocorrelation functions of non-stationary process and itsstationary counterpart. This formula describes the impact of the intra-dayactivity pattern on the autocorrelation function. Furthermore, we applyour model to stationary Continuous-Time Random Walk model with memory, toimprove its agreement with empirical data.