Abstract
Modeling financial time series at different time scales is still an open challenge. The choice of a suitable indicator quantifying the distance between the model and the data is therefore of fundamental importance for selecting models. In this paper, we propose a multiscale model selection method based on the Jensen–Shannon distance in order to select the model that is able to better reproduce the distribution of price changes at different time scales. Specifically, we consider the problem of modeling the ultra high frequency dynamics of an asset with a large tick-to-price ratio. We study the price process at different time scales and compute the Jensen–Shannon distance between the original dataset and different models, showing that the coupling between spread and returns is important to model return distribution at different time scales of observation, ranging from the scale of single transactions to the daily time scale.
Highlights
The complexity of market behavior has fascinated physicists and mathematicians for many years [1].One of the main sources of interest comes from the difficulty of modeling the rich dynamics of assetEntropy 2014, 16 prices
We propose to perform multiscale model selection for financial time series by using the Jensen–Shannon distance [9,10,11], and we consider the case of models describing the high frequency dynamics of large tick assets, i.e., assets where the ratio between tick and price is relatively large [12,13]
The Jensen–Shannon distance analysis that we have performed enables us to perform an accurate test of goodness of our statistical models and to select among a pool of competing models
Summary
The complexity of market behavior has fascinated physicists and mathematicians for many years [1]. A specific challenge is the modeling of how the return distribution changes at different time scales [3]. Since tick size can be a sizable fraction of the asset price, when seen at small time scales, price movement appears as a (non-trivial) random walk on a grid, with jumps occurring at random times, while at large time scales, one can probably forget the microstructural issues and describe the dynamics with a more traditional stochastic differential equation or time series approach. We propose to perform multiscale model selection for financial time series by using the Jensen–Shannon distance [9,10,11], and we consider the case of models describing the high frequency dynamics of large tick assets, i.e., assets where the ratio between tick and price is relatively large [12,13].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
