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Limit theorems for stochastic integrals with long memory processes

Author

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  • Hu, Zhishui
  • Liang, Hanying
  • Wang, Qiying

Abstract

On the convergence to stochastic integrals, semi-martingale structure is imposed in most of previous literature. This semi-martingale structure is restrictive in many statistical and econometric applications, particularly in the field of cointegration. In this paper, we investigate the convergence to stochastic integrals beyond the semi-martingale structure. In particular, we consider the convergence of stochastic integrals with general linear process innovations, allowing for long memory, short memory and antipersistence processes in a unified framework.

Suggested Citation

  • Hu, Zhishui & Liang, Hanying & Wang, Qiying, 2026. "Limit theorems for stochastic integrals with long memory processes," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:spapps:v:195:y:2026:i:c:s0304414926000207
    DOI: 10.1016/j.spa.2026.104888
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    References listed on IDEAS

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