Non-Markov Gaussian Term Structure Models: The Case Of Inflation

Abstract: Standard Gaussian term structure models impose the Markov property: the conditional mean is a function of the risk factors. We relax this assumption and consider models where yields are linear in the conditional mean (but not in the risk factors). To illustrate, yields should span expected inflation but not inflation. Second, expected and surprise yield changes can have opposite contemporaneous effects on expected inflation. Third, the survey forecasts and inflation rate can both be in the state. These three features are inconsistent with the Markov assumption. These effects matter empirically in the USA and in Canada.