Abstract :
The local linear method is popular in estimating nonparametric continuous-time
diffusion models, but it may produce negative results for the diffusion (or volatility)
functions and thus lead to insensible inference. We demonstrate this using U.S.
interest rate data. We propose a new functional estimation method of the diffusion
coefficient based on reweighting the conventional Nadaraya–Watson estimator.
It preserves the appealing bias properties of the local linear estimator and is guaranteed
to be nonnegative in finite samples. A limit theory is developed under mild
requirements (recurrence) of the data generating mechanism without assuming stationarity
or ergodicity.
