On the intraday periodicity duration adjustment of high-frequency data

In the last decade, intensive studies on modeling high frequency financial data at the transaction level have been conducted. In the analysis of high-frequency duration data, it is often the first step to remove the intraday periodicity. Currently the most popular adjustment procedure is the cubic spline procedure proposed by Engle and Russell (1998). In this article, we first carry out a simulation study and show that the performance of the cubic spline procedure is not entirely satisfactory. Then we define periodicity point processes rigorously and prove a time change theorem. A new intraday periodic adjustment procedure is then proposed and its effectiveness is demonstrated in the simulation example. The new approach is easy to implement and well supported by the point process theory. It provides an attractive alternative to the cubic spline procedure.