Abstract We investigate a bivariate pure-jump model of stock prices with long memory in volatility, using a marked log-Gaussian Cox process. We show that, due to the non-synchronicity of transactions, the ordinary least squares estimator of the slope in a contemporaneous regression of returns on returns converges to different targets depending on the sampling frequency. Therefore, we propose a transaction-level estimator that makes full use of data in the complete continuous-time record, and show that the estimator of the slope has slow convergence with rate determined by the memory parameter in volatility.

中文翻译：

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具有长记忆波动率的纯跳跃模型中 α、β 和投资组合权重的估计

摘要 我们使用标记的对数高斯 Cox 过程研究了具有长期波动记忆的股票价格的双变量纯跳跃模型。我们表明，由于交易的非同步性，收益同期回归回归中斜率的普通最小二乘估计会根据采样频率收敛到不同的目标。因此，我们提出了一种交易级估计器，它充分利用了完整连续时间记录中的数据，并表明斜率的估计器与波动率中的记忆参数确定的速率收敛缓慢。