Nonparametric Estimation of the Variance Function in a Structural Break Autoreggressive Model

Seminar abstract

In this paper Dr Yang Zu will consider the non-parametric estimate of the innovation variance function in a structural break autoregressive model that can exhibit unit root, explosive and stationary regimes, allowing for behaviour often seen in financial data where bubble and crash episodes are present.

The model permits multiple regime changes occurring at unknown points in time.

Extant variance function estimators lack consistency for our model. We thus propose a new truncation-based kernel smoothing estimator, which we show is uniformly consistent for the innovation variance function.

Estimation involved two steps;

1. A step where a local least squares estimator is used to estimate the time-varying coefficient of the autoregressive model,
2. where the corresponding local least squares residual series is truncated and used in a kernel smoothing estimator for variance.

Truncation in the second step is the key to achieving consistency. In order to prove the uniform consistency of the variance estimator, we derive sharp uniform rates of convergence for the first step local least squares estimator.

We study the finite sample performance of our estimator and compare it with other estimators in a Monte Carlo simulation.

In an empirical illustration, we show that a popular volatility measure used in financial markets could over-estimate volatility when a financial bubble collapses.

Booking

This event is part of the EBS research seminar series and is a free event. Please come along and bring your friends, classmates and colleagues. 

Speaker bio

Dr Yang Zu is an Assistant Professor in the School of Economics at the University of Nottingham.

He holds a PhD in Econometric from the University of Amsterdam and Tinbergen Institute. He also studied at Wuhan University.

He has published papers in the following journals;

• Journal of Econometrics
• Econometric Theory 
• Econometric Review
• Journal of Empirical Finance

Dr Yang Zu's research interests are in the area of persistent processes, including explosive processes.

His current research includes estimation in the presence of breaks in a variety of stationary and non-stationary processes.