Testing serial correlation in a general d-factor model with possible infinite variance.

Area of Science:

• Econometrics
• Financial Time Series Analysis
• Statistical Inference

Background:

• Serial correlation can lead to inefficient or biased estimations in time series analysis.
• Financial data often exhibits complex error structures, such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) processes.
• Existing methods may struggle with infinite variance issues common in financial modeling.

Purpose of the Study:

• To develop and evaluate novel statistical tests for serial correlation in a general d-factor model with GARCH errors.
• To address challenges posed by infinite variance in financial time series.
• To provide robust tools for accurate time series analysis in econometrics.

Main Methods:

• Development of two empirical likelihood-based testing statistics.
• Asymptotic analysis to establish chi-squared distribution under mild conditions.
• Monte Carlo simulations to assess finite-sample performance.

Main Results:

• Both proposed empirical likelihood statistics are asymptotically chi-squared distributed.
• Simulation results demonstrate excellent finite-sample performance for both tests.
• The tests effectively handle GARCH error processes and potential infinite variance issues.

Conclusions:

• The proposed empirical likelihood-based tests are effective for detecting serial correlation in d-factor models with GARCH errors.
• These tests offer a reliable alternative for financial time series analysis, particularly when dealing with infinite variance.
• The study highlights the practical importance of these tests through an exchange rate impact on stock return analysis.