# Indirect Inference for Locally Stationary Models

## TL;DR

This paper introduces a novel indirect inference approach for complex locally stationary models, enabling inference with nonparametric convergence rates and validated through simulations and financial data analysis.

## Contribution

It develops a local indirect inference algorithm for locally stationary models and establishes their asymptotic properties, addressing nonparametric challenges.

## Key findings

- Validated methodology with simulation studies
- Detected non-linear, time-varying volatility in financial data
- Established asymptotic properties of the estimator

## Abstract

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.