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Goodness‐of‐fit tests for Lévy‐driven Ornstein‐Uhlenbeck processes

Lévy‐Driven Ornstein‐Uhlenbeck (or CAR(1)) processes have been introduced in the literature as a model for stochastic volatility. A general formula to recover the unobserved driving process from a continuously observed CAR(1) was developed. When the CAR(1) process is observed at discrete times, the driving process must be approximated. Approximated increments of the driving process are used to test the hypothesis that the CAR(1) belongs to a specified class of Lévy processes. Two goodness‐of‐fit tests are proposed. The performance of the tests is illustrated through simulation. The Canadian Journal of Statistics 46: 355–376; 2018 © 2018 Statistical Society of Canada