Intra-day variability of the stock market activity versus stationarity of the financial time series

•We used two models to describe the intraday pattern of inter-event times.•We connected estimators of autocorrelation of stationary and non-stationary process.•We proved that day seasonality extends the memory of process and its absolute value.

In this paper we propose a new approach to a well-known phenomena of intra-day activity pattern on the stock market. We suggest that seasonality of inter-transaction times has a more significant impact than intra-day pattern of volatility. Our aim is not to remove the intra-day pattern from the data but to describe its impact on autocorrelation function estimators. We obtain an exact, analytical formula relating estimators of the autocorrelation functions of non-stationary (seasonal) process to its stationary counterpart. Hence, we prove that the day seasonality of inter-transaction times extends the memory of the process. That is, autocorrelation of both, price returns and their absolute values, relaxation to zero is longer.