Specification tests for univariate diffusions

Abstract

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