The Distribution and Quantiles of Sample Autocovariances and Autocorrelations of Sample Moments from a Stationary Process

Key Points

• The aim is to expand on the distribution and quantiles of estimates derived from sample cross-moments of stationary processes.
• Develop expansions for the distribution, density, and quantiles of sample estimates.
• Provide exact, approximate, and asymptotic forms for variance or covariance.
• Illustrate concepts through eight examples including sample autocovariances and autocorrelations.
• Central Limit Theorems extend existing literature, incorporating mean effects and higher-order cross-cumulants.
• Quantiles provided up to magnitude n−r/2 for r=3, enhancing estimation accuracy.
• Demonstrated variations in distribution depending on the chosen estimation method.

Abstract