Abstract

VILLASENOR-ALVA, José A.  and  GONZALEZ-ESTRADA, Elizabeth. Goodness of fit test for brownian movement. Agrociencia [online]. 2006, vol.40, n.2, pp.183-195. ISSN 2521-9766.

In time series analyses of financial data it is important to verify the assumption that the data can be modeled by a Brownian movement process to calculate the price of the risky financial instruments called derivatives. Based on the properties of the Brownian process, three union-intersection-type goodnessof-fit tests are proposed. A Monte-Carlo simulation study was conducted to compare the power of the tests for some given alternative hypotheses of non-Brownian processes and different sizes of data series. The findings show that, in general, the three proposed tests preserve the assigned size; the test based on a combination of runs, Shapiro-Wilk and t, showed to be, in general, the most powerful against the studied alternatives and for almost all the data series sizes considered. Applications were performed on financial data sets.

Keywords : randomness; financial data; Gaussian processes; statistical tests.

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