Physical Sciences and Mathematics Commons^™

Multifractional Brownian Motion And Its Applications To Factor Analysis On Consumer Confidence Index, Christopher Box

CMC Senior Theses

This thesis aims at introducing a new way to model time series objects in statistics using multifractional processes. It provides a detailed review of Brownian motion, fractional Brownian motion and extends the above 2 models to multifractional processes. To demonstrate a successful application to the real world, we perform pattern analysis on consumer confidence and household spending behavior. The analysis is conducted through investigating the local Holder regularity of the consumer confidence index and household expenditure. In the analysis, we first model consumer confidence index and household expenditure with a multifractional stochastic processes. We then use the index, pointwise Holder …