A Pure-Jump Transaction-Level Price Model Yielding Cointegration
提出一个交易级的双变量对数价格模型，通过引入长记忆随机持续时间和跳跃噪声，在交易层面产生分数或标准协整，并证明OLS可一致估计协整参数。
Abstract We propose a new transaction-level bivariate log-price model that yields fractional or standard cointegration. The model provides a link between market microstructure and lower-frequency observations. The two ingredients of our model are a long-memory stochastic duration process for the waiting times, {τk}, between trades and a pair of stationary noise processes, ({ek} and {ηk}), which determine the jump sizes in the pure-jump log-price process. Our model includes feedback between the disturbances of the two log-price series at the transaction level, which induces standard or fractional cointegration for any fixed sampling interval Δt. We prove that the cointegrating parameter can be consistently estimated by the ordinary least squares estimator, and we obtain a lower bound on the rate of convergence. We propose transaction-level method-of-moments estimators of the other parameters in our model and discuss the consistency of these estimators. Keywords: : Information shareLong-memory stochastic durationTick time