Testing for correlation between two time series using a parametric bootstrap

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Traditional methods for time series analysis often focus on mean correlation.
• Assessing variance correlation is crucial for understanding complex financial dynamics.
• Existing tests may lack efficacy in finite sample scenarios.

Purpose of the Study:

• To adapt existing statistical tests for assessing cross-correlation in time series variance.
• To evaluate the performance of these adapted tests, particularly in finite samples.
• To introduce and validate a parametric bootstrapping approach for improved accuracy.

Main Methods:

• Exploration and formal introduction of test statistics for variance cross-correlation.
• Monte Carlo simulations to assess theoretical asymptotic distributions.
• Application and validation of parametric bootstrapping.
• Empirical analysis using financial market data.

Main Results:

• Theoretical asymptotic distributions can be unreliable in finite samples.
• Parametric bootstrapping significantly enhances the accuracy of variance correlation detection.
• The proposed method demonstrates robustness in analyzing financial time series.

Conclusions:

• Parametric bootstrapping is a viable and effective method for time series variance correlation.
• The developed techniques offer a robust approach for financial market analysis.
• This research provides valuable tools for understanding interdependencies in financial data.