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Unformatted text preview: Notes 11 ARCH & GARCH Models 1. Introduction Facts: Many economic time series do not have constant mean and variance. Typical examples: GNP, interest and exchange rates. Definition : Stochastic variables with constant variance are called homoscedastic while those with nonconstant variances heteroscedastic . Remark : The volatility of many series is not constant over time. Series are called conditionally heteroscedastic if the unconditional (or long-run) variance is constant but there are periods in which the variance is relatively high. 2. ARCH Processes (Autoregressive Conditional Heteroscedastic Process) Motivation : 1. Imagine that you are an asset holder! You would be interested in forecast of the rate of return and its variance over the holding period. 2. The unconditional variance (i.e., the long-run forecast of the variance) would be unimportant if you plan to buy the asset at t and sell at t + 1. How to model such phenomenon?...
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- Spring '08