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Register a new userA new approach to the modeling of financial volumes
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In this paper we study the high frequency dynamic of financial volumes of traded stocks by using a semi-Markov approach. More precisely we assume that the intraday logarithmic change of volume is described by a weighted-indexed semi-Markov chain model. Based on this assumptions we show that this model is able to reproduce several empirical facts about volume evolution like time series dependence, intra-daily periodicity and volume asymmetry. Results have been obtained from a real data application to high frequency data from the Italian stock market from first of January 2007 until end of December 2010.
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Fundamental variables in financial market are not only price and return but a very important role is also played by trading volumes. Here we propose a new multivariate model that takes into account price returns, logarithmic variation of trading volumes and also waiting times, the latter to be intended as the time interval between changes in trades, price, and volume of stocks. Our approach is based on a generalization of semi-Markov chains where an endogenous index process is introduced. We also take into account the dependence structure between the above mentioned variables by means of copulae. The proposed model is motivated by empirical evidences which are known in financial literature and that are also confirmed in this work by analysing real data from Italian stock market in the period August 2015 - August 2017. By using Monte Carlo simulations, we show that the model reproduces all these empirical evidences.
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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: Akaikes 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.
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations on different scales, without knowing them in advance. We also present results obtained with this approach while working on Tokyo Stock Exchange intraday quotations. We show that individual sectors and subsectors tend to form important market components which may follow each other with small but significant delays. These components may be recognized by analysing eigenvectors of complex correlation matrix for Nikkei 225 stocks. Interestingly, sectorial components are also found in eigenvectors corresponding to the bulk eigenvalues, traditionally treated as noise.
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