Segmentation algorithm for non-stationary compound Poisson processes

Abstract

Abstract. We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching models of compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.

A Million Metaorder Analysis of Market Impact on the Bitcoin

“…3 3.2), this amounts to studying the ask for buy metaorders and the bid for sell metaorders. The first operation needed in order to study market impact is to spot the metaorders: due to the extreme irregularity and heterogeneity between the traders' typical position paths, usual time series decomposition methods (Toth et al 2010) are not relevant here. In order to identify these large buy and sell metaorders for this particular data, in such a way that no conditioning in the start/end sequences of the metaorders is introduced (most intuitive techniques may create mean-reversion biases), we used the following: For each trader, we defined the start of a metaorder to # of child trades 1 2 ≤ n ≤ 4 5 ≤ n ≤ 9 10 ≤ n % of metaorders 61% 29% 6.5% 3.5% coincide with the first aggressive 5 order placed after a given period of inactivity 6 .…”

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“…Some papers [22,23,24,25,26,27] have investigated databases where it is possible to track the trading behavior of market members of the exchange. Members are credit entities and investment firms which are the only firms entitled to trade directly.…”

“…Therefore they trade on behalf of a large number of investors. Despite this fact, recent studies have shown that, probably due to a customer specialization, market member data allows to identify trading strategies, such as order splitting [23,24,25], liquidity provision [27], and contrarian or momentum trading [22]. In particular in this last study authors have performed an analysis of the linear correlation matrix of the trading activity of market members of the Spanish Stock Exchange in order to identify groups of investors (market members in this case).…”

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