Recurrence interval analysis of high-frequency financial returns and its application to risk estimation

TL;DR

This paper analyzes the recurrence intervals between high-frequency stock returns in China's markets, revealing power-law distributions, memory effects, and applying findings to risk estimation including VaR analysis.

Contribution

It provides a detailed analysis of recurrence interval distributions and memory effects in Chinese stock returns, and applies these insights to improve risk estimation methods.

Findings

Recurrence intervals follow power-law tails.

Symmetry between positive and negative return thresholds.

Memory effects influence recurrence interval dynamics.

Abstract

We investigate the probability distributions of the recurrence intervals $\tau$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures including the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cram\'er-von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds $q$. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability $W_q(\Delta{t},t)$, Value-at-Risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.