Modeling periodic high-frequency intra-day data

High-frequency data typically exhibit periodic patterns in market activity. Furthermore, skewness and kurtosis of financial data has led to development of models with jumps. In order to present a model that supports these features, we introduce a semi-Lévy continuous-time autoregressive moving average (SLCARMA) process. In this paper, we discuss on some properties of such process and estimate the parameters of it by Kalman recursion technique. We fit a SLCARMA(2,1) process to intra-day realized volatility of Doiv Jones industrial average data.