Realized kernels use high-frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same...

The Granger representation theorem states that a cointegrated vector autoregressive process can be decomposed into four components: a random walk, a stationary process, a deterministic part, and a term that depends on the initial values. In this paper, we present a new proof of the theorem. This...

This paper examines the capabilities of the Normal Inverse Gaussian distribu-tion as a model for stock returns. We extend the model of Barndorff-Nielsen (1997) to allow for a richer volatility structure and compare with the existing GARCH-type models. We conclude that the proposed model...