Robust control chart for nonlinear conditionally heteroscedastic time series based on Huber support vector...

Area of Science:

• Statistics
• Time Series Analysis
• Machine Learning

Background:

• Conditionally heteroscedastic time series present challenges for traditional monitoring methods.
• Existing control charts often require complex residual modifications.
• Robust estimation of conditional volatility is crucial for accurate time series analysis.

Purpose of the Study:

• To propose an advanced control chart for monitoring conditionally heteroscedastic time series.
• To integrate Huber support vector regression (HSVR) with one-class classification (OCC) for enhanced monitoring.
• To develop a robust method for estimating conditional volatility in complex time series.

Main Methods:

• Development of the HSVR-GARCH model to incorporate nonlinearity and robustly estimate conditional volatility.
• Construction of a one-class classification (OCC)-based control chart using squared residuals.
• Application of Monte Carlo simulations to evaluate the control chart's performance.
• Utilizing bootstrap methods for control chart construction in real-world financial data.

Main Results:

• The HSVR-GARCH model provides robust conditional volatility estimation, especially in complex, noisy time series.
• The OCC-based control chart using squared residuals eliminates the need for posterior residual modifications.
• Monte Carlo simulations demonstrate significant benefits of the proposed method for complicated and noisy models.
• Real data analysis on Nasdaq and KOSPI indices validates the bootstrap method's efficacy.

Conclusions:

• The proposed HSVR-GARCH integrated OCC control chart offers a robust and effective solution for monitoring conditionally heteroscedastic time series.
• The method is particularly advantageous for complex time series data contaminated with noise.
• The study confirms the practical applicability and validity of the bootstrap method in financial time series control charting.