Modeling financial time series using ARM processes

✍ Scribed by Benjamin Melamed

• Book ID: 104329785
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 866 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00331-5

✦ Synopsis

The class of ARM (Auto-Regressive Modular) processes is a versatile class of nonlinear autoregressive schemes with modulo-1 reduction and additional transformations. It generalizes the class of TES (Transform-Expand-Sample) processes in that it admits dependent innovation sequences. Both TES and ARM processes are designed to produce high-fidelity models from stationary empirical time series by fitting a strong statistical signature consisting of the empirical marginal distribution (histogram) and the empirical autocorrelation function. More specifically, they guarantee the matching of arbitrary empirical distributions and permit the approximation of the leading empirical autocorrelations, simultaneously. This paper provides a brief review of ARM processes and their fundamental properties, and outlines an ARM modeling methodology. It then illustrates the efficacy of financial modeling using the ARM methodology, by fitting TES models to empirical financial data. The models are then applied to the generation of financial Monte Carlo scenarios, and the forecasting of future values via point estimates and confidence intervals.