TL;DR
This paper investigates the asymptotic behavior of log-products of AR(1) processes, providing precise variance calculations and analyzing nonstationary cases to understand their distributional properties.
Contribution
It offers a detailed analysis of the CLT for AR(1) processes, including nonstationary cases, with high-precision variance computations and distributional insights.
Findings
CLT for stationary AR(1) processes established with variance calculations
Distributional analysis of nonstationary AR(1) processes conducted
High-precision variance estimates provided for log-products
Abstract
Given a stationary first-order autoregressive process X_t (with lag-one correlation rho satisfying |rho|<1), we examine the Central Limit Theorem for (1/n)*ln |X_1...X_n| and compute variances to high precision. Given a nonstationary process X_t (with |rho|>1), we examine instead (1/n)*ln|X_n| and study the distribution of ln|X_n|-n*ln|rho|.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFinancial Risk and Volatility Modeling · Statistical Distribution Estimation and Applications · Statistical Methods and Inference