Forecasting and change point test for nonlinear heteroscedastic time series based on support vector regression.

Area of Science:

• Statistics
• Time Series Analysis
• Machine Learning

Background:

• Nonlinear heteroscedastic time series data present challenges for traditional modeling.
• Support Vector Regression-Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (SVR-ARMA-GARCH) models offer flexibility but require robust change point detection.
• Existing methods for change point detection in these models may lack sufficient accuracy and power.

Purpose of the Study:

• To develop and validate advanced methods for change point detection in SVR-ARMA-GARCH models.
• To enhance the accuracy of residual estimation for improved change point detection.
• To increase the detection power of the cumulative sum (CUSUM) test through a novel time-varying control limit approach.

Main Methods:

• Implementation of an alternating recursive estimation (ARE) method for more accurate residual estimation.
• Development of a new CUSUM testing procedure incorporating a time-varying control limit.
• Application and evaluation of proposed methods on simulated and real-world datasets.

Main Results:

• The proposed alternating recursive estimation (ARE) method significantly improves residual estimation accuracy.
• The novel CUSUM test with a time-varying control limit demonstrates enhanced detection power.
• Numerical analyses confirm the effectiveness and superiority of the proposed methods in SVR-ARMA-GARCH models.

Conclusions:

• The developed ARE method and the time-varying control limit CUSUM test are effective for change point detection in SVR-ARMA-GARCH models.
• These methods offer improved accuracy and detection power compared to existing approaches.
• The study validates the proposed techniques through both simulation and a real-world BDI data example.