Lead-Lag Relationships

On lead-lag estimation of non-synchronously observed point processes ArXiv ID: 2601.01871 “View on arXiv” Authors: Takaaki Shiotani, Takaki Hayashi, Yuta Koike Abstract This paper introduces a new theoretical framework for analyzing lead-lag relationships between point processes, with a special focus on applications to high-frequency financial data. In particular, we are interested in lead-lag relationships between two sequences of order arrival timestamps. The seminal work of Dobrev and Schaumburg proposed model-free measures of cross-market trading activity based on cross-counts of timestamps. While their method is known to yield reliable results, it faces limitations because its original formulation inherently relies on discrete-time observations, an issue we address in this study. Specifically, we formulate the problem of estimating lead-lag relationships in two point processes as that of estimating the shape of the cross-pair correlation function (CPCF) of a bivariate stationary point process, a quantity well-studied in the neuroscience and spatial statistics literature. Within this framework, the prevailing lead-lag time is defined as the location of the CPCF’s sharpest peak. Under this interpretation, the peak location in Dobrev and Schaumburg’s cross-market activity measure can be viewed as an estimator of the lead-lag time in the aforementioned sense. We further propose an alternative lead-lag time estimator based on kernel density estimation and show that it possesses desirable theoretical properties and delivers superior numerical performance. Empirical evidence from high-frequency financial data demonstrates the effectiveness of our proposed method. ...

From Data Acquisition to Lag Modeling: Quantitative Exploration of A-Share Market with Low-Coupling System Design ArXiv ID: 2506.19255 “View on arXiv” Authors: Jianyong Fang, Sitong Wu, Junfan Tong Abstract We propose a novel two-stage framework to detect lead-lag relationships in the Chinese A-share market. First, long-term coupling between stocks is measured via daily data using correlation, dynamic time warping, and rank-based metrics. Then, high-frequency data (1-, 5-, and 15-minute) is used to detect statistically significant lead-lag patterns via cross-correlation, Granger causality, and regression models. Our low-coupling modular system supports scalable data processing and improves reproducibility. Results show that strongly coupled stock pairs often exhibit lead-lag effects, especially at finer time scales. These findings provide insights into market microstructure and quantitative trading opportunities. ...

Follow the Leader: Enhancing Systematic Trend-Following Using Network Momentum ArXiv ID: 2501.07135 “View on arXiv” Authors: Unknown Abstract We present a systematic, trend-following strategy, applied to commodity futures markets, that combines univariate trend indicators with cross-sectional trend indicators that capture so-called {"\em momentum spillover"}, which can occur when there is a lead-lag relationship between the trending behaviour of different markets. Our strategy utilises two methods for detecting lead-lag relationships, with a method for computing {"\em network momentum"}, to produce a novel trend-following indicator. We use our new trend indicator to construct a portfolio whose performance we compare to a baseline model which uses only univariate indicators, and demonstrate statistically significant improvements in Sharpe ratio, skewness of returns, and downside performance, using synthetic bootstrapped data samples taken from time-series of actual prices. ...

High-frequency lead-lag relationships in the Chinese stock index futures market: tick-by-tick dynamics of calendar spreads ArXiv ID: 2501.03171 “View on arXiv” Authors: Unknown Abstract Lead-lag relationships, integral to market dynamics, offer valuable insights into the trading behavior of high-frequency traders (HFTs) and the flow of information at a granular level. This paper investigates the lead-lag relationships between stock index futures contracts of different maturities in the Chinese financial futures market (CFFEX). Using high-frequency (tick-by-tick) data, we analyze how price movements in near-month futures contracts influence those in longer-dated contracts, such as next-month, quarterly, and semi-annual contracts. Our findings reveal a consistent pattern of price discovery, with the near-month contract leading the others by one tick, driven primarily by liquidity. Additionally, we identify a negative feedback effect of the “lead-lag spread” on the leading asset, which can predict returns of leading asset. Backtesting results demonstrate the profitability of trading based on the lead-lag spread signal, even after accounting for transaction costs. Altogether, our analysis offers valuable insights to understand and capitalize on the evolving dynamics of futures markets. ...

Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2309.08800 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control, forecasting, and clustering. By understanding the temporal dependencies between different time series, one can better comprehend the complex interactions and patterns within the system. We develop a cluster-driven methodology based on dynamic time warping for robust detection of lead-lag relationships in lagged multi-factor models. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our algorithm is able to robustly detect lead-lag relationships in financial markets, which can be subsequently leveraged in trading strategies with significant economic benefits. ...

Robust Detection of Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2305.06704 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clustering. We develop a clustering-driven methodology for robust detection of lead-lag relationships in lagged multi-factor models. Within our framework, the envisioned pipeline takes as input a set of time series, and creates an enlarged universe of extracted subsequence time series from each input time series, via a sliding window approach. This is then followed by an application of various clustering techniques, (such as k-means++ and spectral clustering), employing a variety of pairwise similarity measures, including nonlinear ones. Once the clusters have been extracted, lead-lag estimates across clusters are robustly aggregated to enhance the identification of the consistent relationships in the original universe. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our method is not only able to robustly detect lead-lag relationships in financial markets, but can also yield insightful results when applied to an environmental data set. ...