Quasi-Maximum Exponential Likelihood Estimation of Conditional Quantiles for GARCH Models Based on High-Frequency...

Area of Science:

• Econometrics
• Financial Modeling
• Time Series Analysis

Background:

• Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are crucial for analyzing time-varying financial volatility.
• Financial returns often exhibit heavy-tailed distributions, necessitating methods like quasi-maximum exponential likelihood estimation (QMELE) for accurate tail behavior and risk measure estimation (e.g., Value-at-Risk).
• High-frequency data offers intraday volatility dynamics and market microstructure insights beyond traditional low-frequency observations.

Purpose of the Study:

• To develop and analyze conditional quantile estimation for high-frequency augmented GARCH models.
• To propose QMELE-based estimators for model parameters and conditional quantiles.
• To introduce an adjusted test statistic for evaluating model adequacy.

Main Methods:

• Development of quasi-maximum exponential likelihood estimation (QMELE) for parameter and quantile estimation.
• Construction of an adjusted test statistic for model adequacy assessment.
• Establishment of asymptotic properties for estimators and the test statistic, followed by simulation studies.

Main Results:

• The proposed QMELE-based estimators and adjusted test statistic demonstrate strong theoretical properties.
• Simulation studies confirm the finite-sample performance of the developed methods.
• Empirical analysis on major stock indices shows significant improvements in conditional quantile estimation using high-frequency augmented GARCH models.

Conclusions:

• Augmenting GARCH models with high-frequency data substantially enhances conditional quantile estimation accuracy.
• The QMELE approach effectively captures tail behavior and improves risk management insights.
• The developed methodology provides a robust framework for analyzing financial volatility with high-frequency data.