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Type I and Type II Errors in the Unit Root Determination of a Fractional Brownian Motion AgEcon
Wongsasutthikul, Paitoon; Turvey, Calum G.; Power, Gabriel J..
Economists who deal with time-series data usually take the unit root test as the ‘prerequisite’ test for a Brownian motion. It is typical for any researchers to apply a battery of well-known unit root tests to their models to confirm stationarity in the model specification. Nonetheless, often times, we see a conclusion that fail to reject the null in favor of the existence of unit root even though the model specification is such that the lag coefficients of an AR(q) process do not sum up to unity. In this study, we show that having the sum of the lag coefficients equals to unity is indeed a necessary and sufficient condition for the existence of a unit root. Hence, the aforementioned incident will lead to a type II error in the unit root determination. On...
Tipo: Conference Paper or Presentation Palavras-chave: Unit root; Hurst exponent; Fractional Brownian Motion; Financial Economics; Risk and Uncertainty.
Ano: 2010 URL: http://purl.umn.edu/60984
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