Modeling Tail Index With Autoregressive Conditional Pareto Model

Abstract

We propose an autoregressive conditional Pareto (AcP) model based on the dynamic peaks over threshold method to model a dynamic tail index in the financial markets. Unlike the score-based approach which is widely used in many articles, we use an exponential function to model the tail index process for its intuitiveness and interpretability. Probabilistic properties of the AcP model and the statistical properties of its parameter estimators of maximum likelihood are studied in this article. Real data are used to show the advantages of AcP, especially, compared to the estimation volatility of GARCH model, the result of AcP is more sensitive to turmoil. The estimated tail index of AcP can accurately reflect the risk of the stock and may even play an early warning role to the turmoil of stock market. We also calculate the tail connectedness based on the estimated tail index of AcP and show that tail connectedness increases during period of turmoil, which is consistent with the result of the score-based approach.