In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit...

By studying the differences between futures prices and exchange-traded fund prices for the S&P 500 index, original results are obtained about the distribution and persistence of the microstructure noise component created by bid/ask spreads and discrete price scales. The bivariate density of this...

We propose several nonparametric predictors of the mid-price in a limit order book, based on different features constructed from the order book data observed contemporaneously and in the recent past. We evaluate our predictors in the context of an order execution task by constructing order...

This paper proposes an accurate, parsimonious and fast-to-estimate forecasting model for integer-valued time series with long memory and seasonality. The modelling is achieved through an autoregressive Poisson process with a predictable stochastic intensity that is determined by two factors: a...

The Regression Tree (RT) sorts the samples using a specific feature and finds the split point that produces the maximum variance reduction from a node to its children. Our key observation is that the best factor to use (in terms of MSE drop) is always the target itself, as this most clearly...