Modelling bid-ask spread conditional distributions using hierarchical correlation reconstruction

• Authors: Jarosław Duda , Henryk Gurgul , Robert Syrek

Abstracts

EN

While we would like to predict exact values, the information available, being incomplete, is rarely sufficient - usually allowing only conditional probability distributions to be predicted. This article discusses hierarchical correlation reconstruction (HCR) methodology for such a prediction using the example of bid-ask spreads (usually unavailable), but here predicted from more accessible data like closing price, volume, high/low price and returns. Using HCR methodology, as in copula theory, we first normalized marginal distributions so that they were nearly uniform. Then we modelled joint densities as linear combinations of orthonormal polynomials, obtaining their decomposition into mixed moments. Then we modelled each moment of the predicted variable separately as a linear combination of mixed moments of known variables using least squares linear regression. By combining these predicted moments, we obtained the predicted density as a polynomial, for which we can e.g. calculate the expected value, but also the variance to determine the uncertainty of the prediction, or we can use the entire distribution for, e.g. more accurate further calculations or generating random values. 10-fold cross-validation log-likelihood tests were conducted for 22 DAX companies, leading to very accurate predictions, especially when individual models were used for each company, as significant differences were found between their behaviours. An additional advantage of using this methodology is that it is computationally inexpensive; estimating and evaluating a model with hundreds of parameters and thousands of data points by means of this methodology takes only a second on a computer.

Keywords

EN

machine learning; conditional distribution; bid-ask spread; liquidity

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2020
• Volume: 21
• Issue: 5
• Pages: 99-118

Contributors

author

Jarosław Duda

• Jagiellonian University, Poland

• https://orcid.org/000000019559809X

author

Henryk Gurgul

• AGH University of Science and Technology, Poland

• https://orcid.org/0000000261922995

author

Robert Syrek

• Jagiellonian University, Poland

• https://orcid.org/0000000282128248

Identifiers

DOI

10.21307/stattrans-2020-057

Biblioteka Nauki

1059037