Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A framework for the modeling of order book dynamics based on event sizes   We propose a modeling framework for the dynamics of a reduced form order book
in event time and based on event sizes. Our framework for the order book is
influenced by [9], but compared to [9] we allow the best bid ask spread to be
larger than one tick. Based on the modeling assumption that the best bid as
well as the best ask price can only move by at most one tick (up or down), when
an event occurs, we show that the dynamics of this simplified order book is
completely described by a non-linear transformation of two processes (X, Y ). A
key challenge in the modeling is the empirical fact that the high frequency
order flow is strongly autocorrelated, a fact we have to deal with in the
modeling of (X, Y ). The core of our framework is a semi linear regression type
model for (X, Y ), influence by more classical ARMA and AR models, and one key
degree of freedom is the potentially non-linear basis functions used in the
regression. We use results from the theory of random iterative function systems
to understand issues concerning stationarity and ergodicity in our models. We
show how to rapidly calibrate the model by inverting block Toeplitz matrices in
an efficient way. All components are worked through and explain in an
application and the predictability of the model for order flows and price moves
are analyzed in the context of a high frequency dataset.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph