Dynamic Models of Asset Returns and Their Volatilities
In Chapter 3 on single-period investment theories, historical asset returns are assumed to be i.i.d. This assumption, however, is sometimes violated, as illustrated in Section 5.1.2. On the other hand, since the historical asset returns are only used as a random sample to estimate the mean and covariance matrix of the asset returns in the single period for which investment plans are made, this simplified i.i.d. assumption is innocuous if one does not go too far back into the past, during which structural changes may have occurred.
Since subsequent chapters on finance models and applications will involve the dynamic evolution of asset returns and their volatilities, we consider here various statistical methods and models that have been developed to analyze these time series data. Although traditional time series methods such as those in Chapter 5 suffice for the dynamic levels of asset returns, they do not capture observed patterns of time-varying volatilities and volatility clustering in financial time series. Section 6.1 describes these patterns, often called stylized facts, of asset returns and their volatilities.
KeywordsAsset Return GARCH Model Exponentially Weighted Move Average Return Series Standard Normal Random Variable
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