Inference for local autocorrelations in locally stationary models.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Non-stationary processes exhibit changing correlation structures, crucial for understanding dynamic systems.
• Traditional methods often assume stationarity, limiting analysis of real-world time series.
• Local autocorrelation captures evolving dependencies within time series data.

Purpose of the Study:

• To develop methods for estimating and inferring local autocorrelation in locally stationary time series.
• To provide tools for hypothesis testing on time-varying autocorrelation.
• To generalize existing autocorrelation functions (e.g., R's acf()) to locally stationary Gaussian processes.

Main Methods:

• Development of simultaneous confidence bands for local autocorrelation.
• Application of statistical inference techniques to time series data.
• Utilizing simulation studies to validate the proposed methodology.

Main Results:

• Demonstrated time-varying local autocorrelations in global temperature data with a distinct "V" shape between 1910-1960.
• Confirmed that S&P 500 index returns align with the efficient-market hypothesis.
• Identified significant local autocorrelations in the magnitudes of S&P 500 returns.

Conclusions:

• The proposed methods effectively detect and quantify time-varying local autocorrelations.
• Empirical results highlight the dynamic nature of correlations in economic and climate data.
• The findings extend the applicability of autocorrelation analysis to a broader class of non-stationary processes.