Image credit: UnsplashAbstract
Unit root model has wide application in mathematical finance, many mathematical models view unit root process as the variable data generation process, and stochastic unit root model on the basis of unit root process relax the certainty of coefficient of unit root hypothesis, it will introduce the new information to the model, making unit root has a certain randomness, this model is more general. Due to the financial data generally have the characteristics of the thick tail, this article selects a simple linear stochastic model of unit root, the normal distribution assumption has been generalized to the generalized error distribution, and the model of steady condition, the maximum likelihood estimation and stochastic unit root hypothesis test has carried on the discussion, finally we gives strictly stationary and weakly stationary condition, solving the maximum likelihood estimators of two kinds of algorithm (parametric and EM algorithm) as well as the two random unit root hypothesis test ideas (LM test and Wald test).
