Exploring Financial Statements and Fraud Using Topological Tests

• In Event: Forensic and Investigative Accounting

Abstract

The purpose of this study was to explore financial statement data of both fraudulent and non-fraudulent firms for evidence of non-linearity. A longitudinal examination of ten financial ratios computed from quarterly income statement and balance sheet data was conducted for 30 matched pairs of firms. Using chaos theory methodology, topological tests were performed to determine the behavior of the time-series (i.e., random, periodic, or chaotic). The results of the tests indicate that the following ratios were consistently strong indicators of chaos: fixed assets to total assets; total liabilities to total assets; current assets to current liabilities. These findings indicate that ratios comprised of financial data as reported on the balance sheet are the result of non-linear chaotic dynamics. The use of linear models derived from financial ratios based on balance sheet data is inappropriate. Such models do not robustly represent the system and result in low explanatory power. This study examined the qualitative changes in financial ratios across time and found no differences in dynamics between fraudulent and non-fraudulent firms, thereby providing further evidence of the limited ability of financial ratios to detect fraudulent firms.

Author

• Kathleen A Kaminski, Kutztown University of Penn