Hybrid CUSUM Change Point Test for Time Series with Time-Varying Volatilities Based on Support Vector Regression.

Area of Science:

• Time Series Analysis
• Econometrics
• Machine Learning

Background:

• Detecting changes in conditional variance is crucial for financial time series analysis.
• Traditional methods may not adequately capture time-varying volatilities.
• Accurate volatility estimation is essential for risk management and forecasting.

Purpose of the Study:

• To develop and validate a novel cumulative sum (CUSUM) of squares test for detecting conditional variance changes.
• To integrate Support Vector Regression (SVR) with Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models for improved residual analysis.
• To assess the performance of the proposed test using simulations and real-world financial data.

Main Methods:

• Fitting SVR-GARCH models with varying tuning parameters on training data.
• Selecting the optimal SVR-GARCH model using a validation set.
• Constructing the residual CUSUM of squares test using residuals and conditional volatility estimates from the best model.
• Conducting Monte Carlo simulations with linear and nonlinear GARCH models.

Main Results:

• The proposed residual CUSUM of squares test demonstrates validity in detecting conditional variance changes.
• The SVR-GARCH modeling approach effectively captures time-varying volatilities.
• Simulations confirm the test's performance across different GARCH model specifications.

Conclusions:

• The developed SVR-GARCH-based CUSUM test is a viable tool for detecting volatility shifts in time series.
• The method shows practical applicability in analyzing financial market data.
• This approach enhances the analysis of financial time series with time-varying volatilities.