# The application of co-integration theory in ensemble pulsar timescale algorithm

## TL;DR

This paper introduces a co-integration theory-based algorithm for ensemble pulsar timescale construction, effectively reducing noise and enhancing long-term stability by including pulsars with significant red noises.

## Contribution

It proposes a novel co-integration based approach that allows pulsars with red noise to participate in ensemble timescale estimation, improving stability over classical methods.

## Key findings

- Reduces timing noise in pulsar data
- Improves long-term stability of ensemble pulsar timescale
- Enables inclusion of pulsars with red noise

## Abstract

Employing multiple pulsars and using an appropriate algorithm to establish ensemble pulsar timescale can reduce the influences of various noises on the long-term stability of pulsar timescale, compared to a single pulsar. However, due to the low timing precision and the significant red noises of some pulsars, their participation in the construction of ensemble pulsar timescale is often limited. Inspired by the principle of solving non-stationary sequence modeling using co-integration theory, we puts forward an algorithm based on the co-integration theory to establish ensemble pulsar timescale. It is found that this algorithm can effectively suppress some noise sources if a co-integration relationship between different pulsar data exist. Different from the classical weighted average algorithm, the co-integration method provides the chances of the pulsar with significant red noises to attend the establishment of ensemble pulsar timescale. Based on the data from the North American Nanohertz Observatory for Gravitational Waves, we found that the co-integration algorithm can successfully reduce several timing noises and improve the long-term stability of the ensemble pulsar timescale.