Multiscale Model Selection for High-Frequency Financial Data of a Large Tick Stock by Means of the Jensen–Shannon Metric

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.

An Information Theoretic Criterion for Empirical Validation of Time Series Models

“…The L-div is estimated for all available lengths of the time-window and results are finally aggregated into a single information criterion, the Generalized Subtracted Ldivergence (shortly GSL-div ). Our approach can be seen as an extension of the work provided in [15], where the Jensen-Shannon divergence is used to measure the distance between distributions of single observations at different aggregation scales, and [42], where time series are symbolized in a similar way.…”

“…It is to be noticed that the estimation of B is, in general, non-trivial [50]. In [32,54,15] the number of states in the support of p are approximated by the number of states occurring with non-zero frequency. However this approach could be totally misleading, in particular if the series are non-stationary.…”