A test of financial time-series data to discriminate among lognormal, Gaussian and square-root random walks

Abstract

This paper aims to offer a testing framework for the structural properties of the Brownian motion of the underlying stochastic process of a time series. In particular, the test can be applied to financial time-series data and discriminate among the lognormal random walk used in the Black-Scholes-Merton model, the Gaussian random walk used in the Ornstein-Uhlenbeck stochastic process, and the square-root random walk used in the Cox, Ingersoll and Ross process. Alpha-level hypothesis testing is provided. This testing framework is helpful for selecting the best stochastic processes for pricing contingent claims and risk management.