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Statistical Inference for Unified Garch–Itô Models with High‐Frequency Financial Data
Author(s) -
Kim Donggyu
Publication year - 2016
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12171
Subject(s) - estimator , econometrics , mathematics , autoregressive conditional heteroskedasticity , volatility (finance) , consistency (knowledge bases) , likelihood function , strong consistency , statistical inference , inference , indirect inference , statistics , maximum likelihood , computer science , artificial intelligence , geometry
The existing estimation methods for the model parameters of the unified GARCH–Itô model (Kim and Wang, [Kim D, 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.