  We propose the use of indirect inference estimation to conduct inference in
complex locally stationary models. We develop a local indirect inference
algorithm and establish the asymptotic properties of the proposed estimator.
Due to the nonparametric nature of locally stationary models, the resulting
indirect inference estimator exhibits nonparametric rates of convergence. We
validate our methodology with simulation studies in the confines of a locally
stationary moving average model and a new locally stationary multiplicative
stochastic volatility model. Using this indirect inference methodology and the
new locally stationary volatility model, we obtain evidence of non-linear,
time-varying volatility trends for monthly returns on several Fama-French
portfolios.
