Atomic Decomposition of Financial Data

• Authors: Seth A. Greenblatt
• Venue: Computational Economics - Special issue on numerical methods in economics and finance
• Year: 1998

When looking at a time series, it is often instructive to consider thedata as observations sampled from a noisy version of some underlying datagenerating process. This data generating process may be considered to be afunction from a function space. We can specify very simple functions, knownas atoms, which may be taken in linear combinations to represent anyfunction within a particular function space. The atoms are described asmembers of a family of functions indexed by parameters. Quite commonly usedfor functions underlying time series data are the parameters location andfrequency. This type of atom is known as a time-frequency atom. After wehave specified the family of atoms that we wish to use to represent ourunderlying data generating process, the difficult problem of choosing themost effective, parsimonious representation from this family remains to besolved. Several techniques, such as Matching Pursuit and Basis Pursuit, havebeen suggested to solve this problem. In the current study, we investigatethe use of several families of atoms, both individually and in combination,to decompose exchange rate data in search of structure that has beenoverlooked in more traditional approaches.