Central Limit Theorems for Conditional Markov Chains

This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means themselves are asymptotically normally distributed, an unconditional Central Limit Theorem can be obtained. The methodology is used to construct a statistical hypothesis test which is applied to synthetically generated environmental data.