文章基本信息

标题：Contemporaneous Aggregation of GARCH Processes
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作者：Paolo Zaffaroni
期刊名称：Distributional Analysis Publications
印刷版ISSN：1352-2469
出版年度：2000
卷号：2000
出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：We study the impact of large cross-sections of contemporaneous aggregation ofGARCH processes and of dynamic GARCH factor models. The results cruciallydepend on the shape of the cross-sectional distribution of the GARCHcoefficients and on the cross-sectional dependence properties of the rescaledinnovation. The aggregate maintains the core nonlinearity of a volatility model,uncorrelation in the levels but autocorrelation in the squares, when the rescaledinnovation is common across units. The nonlinearity is, however, lost at theaggregate level, when the rescaled innovation is orthogonal across units. This isnot a consequence of the usual result of a vanishing importance of purelyidiosyncratic risk as, under appropriate conditions, this is simply not fullydiversifiable in arbitrary large portfolios. Non-GARCH memory properties arise atthe aggregate level. Strict stationarity, ergodicity and finite kurtosis might fail forthe aggregate despite the micro GARCH do satisfy these properties. Under noconditions aggregation of GARCH induces long memory conditionalheteroskedasticity.
关键词：Contemporaneous aggregation; GARCH; conditionally;heteroskedastic factor models; common and idiosyncratic risk; nonlinearity;memory.