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Mailan Trinh

Publications and source records attributed to Mailan Trinh.

2 recordsLinked to original sources
arXiv2017

Limit Theorems for the Fractional Non-homogeneous Poisson Process

The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $α$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional non-homogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.

math.PR↗
arXiv2017

Modeling non-stationarities in high-frequency financial time series

We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a consequence of the empirical analyses, we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process. We test this model against the empirical findings and it turns out that the model can approximately reproduce several stylized facts of high-frequency financial time series. Moreover, using Monte Carlo simulations, we analyze order selection for this model class using three information criteria: Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn information criterion (HQ). For comparison, we also perform a similar Monte Carlo experiment for the ACD (autoregressive conditional duration) model. Our results show that the information criteria work best for small parameter numbers for the compound Poisson type models, whereas for the ACD model the model selection procedure does not work well in certain cases.

q-fin.ST↗