Ten simulated price series for the 19 trading days in January 2010:
Ten hypothetical price series were simulated according to the factor diffusion process discussed in Barndorff-Nielsen et al. We assume that prices are only observed when a transaction takes place. The intensity of transactions follows a Poisson process and consequently, the inter transaction times are exponentially distributed. Therefore, we generated the inter transaction times of the price series by an independent exponential distributions with lambda = 0.1, which we keep constant over time. This means we expect one transaction every ten seconds. In a final step, the time series were aggregated to the 5-minute frequency by previous tick aggregation.
Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde and N. Shephard (2009). Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. Journal of Econometrics, forthcoming.