Indirect inference for locally stationary models

David T Frazier,Bonsoo Koo

doi:10.1016/j.jeconom.2020.08.004

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.

Highlights

Time-varying economic and financial variables, and relationships thereof, are stable features in applied econometrics
To circumvent the above issue, and to help proliferate the use of locally stationary models and methods in econometrics and finance, we propose a novel nonparametric indirect inference method to estimate locally stationary processes
None of the estimated leverage effects are statistically significant for the short-term volatility process. To ensure that this insignificance is not an artifact of the chosen auxiliary model, in Table 3 we report 99% confidence intervals for the corresponding LS-GJR-GARCH auxiliary parameter γ, which captures the impact of asymmetric news on volatility, and where the confidence intervals are calculated using QMLE sandwich form standard errors

Summary

Introduction

Time-varying economic and financial variables, and relationships thereof, are stable features in applied econometrics. Notable examples include asset pricing models with time-varying features (Ghysels, 1998; Wang, 2003) and trending macroeconomic models (Stock and Watson, 1998; Phillips, 2001). While classical analyses of time series are built on the assumption of stationarity, data studied in finance and economics often exhibit nonstationary features. Many different schools of modeling and estimation methods are used to accommodate the nonstationary behavior of observed time series data. Statistical tools developed for locally stationary processes provide a convenient means of conducting analyses of trending economic and financial models. Local stationarity implies that a process behaves in a stationary manner (at least) in the vicinity of a given time point but could be nonstationary over the entire time horizon. For certain widelystudied time series models, slowly time-varying parameters ensure local stationarity under some regularity conditions; for instance, see Dahlhaus (1996) and Dahlhaus (1997) (AR(1)), Dahlhaus and Subba Rao (2006) (ARCH(∞)), Dahlhaus and Polonik (2009) (MA(∞)), Koo and Linton (2012) (Diffusion processes) and Koo and Linton (2015) (GARCH(1,1) with a time-varying unconditional variance) among many other classes of locally stationary processes

Objectives

Methods

Conclusion