Estimation and tests for power-transformed and threshold GARCH models.

Area of Science:

• * Econometrics
• * Time Series Analysis
• * Financial Modeling

Background:

• * The standard GARCH model has limitations in capturing complex financial data characteristics.
• * Existing models like the power-transformed and threshold GARCH(1,1) require further generalization.
• * Financial time series often exhibit heavy-tailed error distributions, posing estimation challenges.

Purpose of the Study:

• * To introduce and analyze the Power-Transformed and Threshold GARCH (PTTGARCH) model.
• * To develop and validate robust estimation methods for PTTGARCH models, especially under heavy-tailed error distributions.
• * To enable statistical inference and model selection for PTTGARCH models in practical applications.

Main Methods:

• * Establishing asymptotic normality for Quasi-Maximum Likelihood Estimators (QMLE) under finite fourth moment conditions.
• * Proposing and proving asymptotic normality for Least Absolute Deviations Estimation (LADE) under weak moment conditions for heavy-tailed errors.
• * Applying the PTTGARCH model to analyze the daily returns of the Hong Kong Hang Seng Index.

Main Results:

• * Asymptotic normality is established for QMLE and LADE of PTTGARCH parameters.
• * LADE demonstrates superior accuracy compared to QMLE for heavy-tailed errors.
• * The PTTGARCH model effectively captures asymmetry and nonlinearity in financial time series, as evidenced by the Hong Kong Hang Seng Index data.

Conclusions:

• * The PTTGARCH model provides a flexible framework for modeling financial time series with complex error distributions.
• * LADE offers a robust and accurate estimation method for PTTGARCH models, particularly in the presence of heavy tails.
• * The study facilitates statistical inference and model selection for PTTGARCH models, enhancing their applicability in financial econometrics.