Semiparametric Estimation of AR-ARCH Models with Measurement Error

• Activity Number: 220
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Liqun Wang*
• Companies: University of Manitoba

Abstract

Dynamic model with autoregressive heteroscedastic (ARCH) error and its various generalizations have been widely used at analyze economic and financial data. Although it is well-known that many economic variables such as GDP, inflation, commodity prices and high-frequency stock prices are measured imprecisely, the statical problems of measurement error have not been investigated in the literature. In this paper we study an autoregressive model with ARCH error where the underlying process is latent and subject to additive measurement error. Based on the observations of a proxy process we construct semiparametric estimators using the GMM framework. We also discuss the issue of identifiability. The proposed estimators are consistent and asymptotically normally distributed under fairly general regularity conditions. We also propose a procedure to test the presence of measurement error. We carry out Monte Carlo simulations to study the impact of measurement error on the naive maximum likelihood estimator, and to study the finite sample properties of our proposed estimators.