We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We find that non-stationarities detected in other markets in the past are still there. Moreover , scaling properties reported in the previous literature for other high-frequency financial data are approximately valid as well. Finally , we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process and we test this model against the empirical findings . It turns out that the model can  reproduce several stylized facts of 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 .
R
find that non-stationarities detected in other markets in the past are still there. Moreover
can confirm previously detected non-stationarities. However
R
approximately valid as well. Finally
only approximately valid. As a consequence of the empirical analyses
R
and we
. We
R
. It
and it
A
approximately
A
. 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