报告题目： Identifiability and Estimation of dynamic ARCH Models with Measurement Error
报告简介：The autoregressive conditional heteroscedasticity (ARCH) model and its various generalizations have been widely used to analyze economic and financial data. Although many variables like GDP, inflation and commodity prices are imprecisely measured, the problem of measurement error in ARCH-type models has not been studied in the literature. We study an autoregressive model with ARCH error where the underlying process is latent and subject to additive measurement error. We show that, in contrast to the case of covariate measurement error in regression models, this model is identifiable by using the observations of a proxy process only and no extra information is needed. We propose GMM estimators for the unknown parameters that are consistent and asymptotically normally distributed under general conditions. We also propose a procedure to test the presence of measurement error, which avoids the usual boundary problem of testing variance parameters. We carry out Monte Carlo simulations to study the impact of measurement error on the naive maximum likelihood estimators and have found interesting evidence of possible mathematical formulas of the biases. Moreover, the proposed estimators have fairly good finite sample properties.