Specification tests for univariate diffusions

A new class of specification tests for stochastic differential equations (SDE) is proposed to determine whether the probability integral transform estimated model generates an independent and identically distributed uniform random variable. The are based on Neyman’s smooth test, appropriately adjusted correct both size distortion arising from having estimate unknown parameters SDE possible dependence in suite compared against other commonly used SDEs. finite sample properties investigated using a range Monte Carlo experiments. then applied testing SDEs spot interest rate financial asset volatility.