Continuous-time Garch processes

• 成果类型: Article
• 署名作者: Brockwell, Peter; Chadraa, Erdenebaatar; Lindner, Alexander
• 署名单位: Colorado State University System; Colorado State University Fort Collins; Technical University of Munich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000150
• 发表日期: 2006
• 页码: 790-826
• 关键词: Stationarity; driven; models

摘要

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the COGARCH(1, 1) process of Kluppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601-622], is introduced and studied. The resulting COGARCH(p, q) processes, q >= p >= 1, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than those of the COGARCH(1, 1) process. We establish sufficient conditions for the existence of a strictly stationary nonnegative solution of the equations for the volatility process and, under conditions which ensure the finiteness of the required moments, determine the autocorrelation functions of both the volatility and the squared increment processes. The volatility process is found to have the autocorrelation function of a continuous-time autoregressive moving average process.