Multiresolution analysis of long time series with applications to finance

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolution and averaging over shorter intervals lead to a finer resolution. Arranging sub-intervals of given lengths on scales with coarse to fine resolution imply a structure which can be represented as a directed acyclic graph. Time series models are then formulated using this graph structure. It is shown that these models have a linear state space representation which allows for efficient computation of the likelihood needed in parameter estimation and for a straightforward treatment of missing observations. Application of these models to the log transaction prices of the IBM shares traded at the New York Stock Exchange from February until October 2002 show that the corresponding one-step prediction errors are heavy tailed and therefore a specific variance term is allowed to follow a fiEGARCH specification, improving the tail behavior and leading to a better fit.