On lead-lag estimation of non-synchronously observed point processes
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arXiv
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| Format: | Preprint |
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2026
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| author | Shiotani, Takaaki Hayashi, Takaki Koike, Yuta |
| author_facet | Shiotani, Takaaki Hayashi, Takaki Koike, Yuta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On lead-lag estimation of non-synchronously observed point processes Shiotani, Takaaki Hayashi, Takaki Koike, Yuta Statistics Theory Statistical Finance Methodology 62M10 (Primary), 62G05, 60G55 (Secondary) 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. |
| title | On lead-lag estimation of non-synchronously observed point processes |
| topic | Statistics Theory Statistical Finance Methodology 62M10 (Primary), 62G05, 60G55 (Secondary) |
| url | https://arxiv.org/abs/2601.01871 |