Bootstrapping a powerful mixed portmanteau test for time series

Area of Science:

• Statistics
• Econometrics
• Environmental Science

Background:

• Time series analysis often requires distinguishing linear from nonlinear dynamics.
• Existing methods for nonlinearity detection may lack power or rely on strict assumptions.

Purpose of the Study:

• To introduce a new portmanteau test statistic for improved nonlinearity detection in time series.
• To evaluate the performance of the proposed test against established methods.

Main Methods:

• A novel portmanteau test statistic is proposed, based on the determinant of a matrix of residual autocorrelations and squared residuals.
• The asymptotic distribution is derived, approximated by a gamma distribution, and a bootstrapping approach is employed for robustness.
• The test's efficacy is assessed using stationary time series models with linear and nonlinear dependency structures.

Main Results:

• The proposed test statistic demonstrates effectiveness in detecting nonlinearity.
• The test exhibits higher statistical power compared to existing methods in various scenarios.
• The approach is robust to relaxed distributional assumptions through bootstrapping.

Conclusions:

• The new portmanteau test provides a powerful tool for nonlinearity detection in time series analysis.
• The test is advantageous for analyzing complex dependencies in economic and environmental data.