Statistical Inference for Unified Garch–Itô Models with High‐Frequency Financial Data. (29th November 2015)

• Record Type: Journal Article
• Authors: Kim, Donggyu
• Is Part Of: Journal of time series analysis. Volume 37:Number 4(2016:Jul.)
• Page Start: 513
• Page End: 532
• Publication Date: 2015-11-29
• Subjects: GARCH -- high‐frequency financial data -- low‐frequency financial data -- Itô process -- quasi‐maximum likelihood estimator -- realized volatility; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12171
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : The existing estimation methods for the model parameters of the unified GARCH–Itô model (Kim and Wang, 2014 ) require long period observations to obtain the consistency. However, in practice, it is hard to believe that the structure of a stock price is stable during such a long period. In this article, we introduce an estimation method for the model parameters based on the high‐frequency financial data with a finite observation period. In particular, we establish a quasi‐likelihood function for daily integrated volatilities, and realized volatility estimators are adopted to estimate the integrated volatilities. The model parameters are estimated by maximizing the quasi‐likelihood function. We establish asymptotic theories for the proposed estimator. A simulation study is conducted to check the finite sample performance of the proposed estimator. We apply the proposed estimation approach to the Bank of America stock price data.