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

TL;DR

This paper investigates how intra-day activity patterns influence the autocorrelation estimation in financial time series, revealing that daily seasonality extends the apparent memory of the process and affects its relaxation behavior.

Contribution

It provides an exact formula linking autocorrelation estimators of non-stationary and stationary processes, highlighting the impact of intra-day seasonality on process memory.

Findings

Intra-day activity patterns extend the autocorrelation decay time.

Seasonality in transaction times influences the perceived memory of the process.

The paper derives an exact relation between non-stationary and stationary autocorrelation estimators.

Abstract

We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart. Hence, we proved that the day seasonality of inter-transaction times extends the memory of as well the process itself as its absolute value. That is, both processes relaxation to zero is longer.