ARCH - AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY(ARCH...

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AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY (ARCH) MODEL HAKAN YILMAZKUDAY
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Autoregressive Conditional Heteroskedasticity (ARCH) Model 2 AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY (ARCH) MODEL The main idea of this paper is that volatility matters, whether it is in determining, for example, asset prices, exchange rates, inflation or wage determination. 1. ECONOMIC TIME SERIES: THE STYLIZED FACTS 1 For series exhibiting volatility, the unconditional variance may be constant even though the variance during some periods is unusually large. Sometimes, only conditional variance is important for us. For instance, as an asset holder, we would be interested in forecasts of the rate of return and its variance over the holding period. 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 . 1 This section draws on Walter Enders, “ Applied Econometric Time Series .
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Autoregressive Conditional Heteroskedasticity (ARCH) Model 3 Some sample means do not appear to be constant and/or there is the strong appearance of heteroskedasticity. We can characterize the key features of the various series with “stylized facts”. So what is a stylized fact? As revealed by a casual examination of most financial newspapers and journals, the view point of many market analysts has been and remains an event-based approach in which one attempts to ‘explain’ or rationalize a given market movement by relating it to an economic or political event or announcement. From this point of view, one could easily imagine that, since different assets are not necessarily influenced by the same events or information sets, price series obtained from different assets and — a fortiori — from different markets will exhibit different properties. After all, why should properties of corn futures be similar to those of IBM shares or the Dollar/Yen exchange rate? Nevertheless, the result of more than half a century of empirical studies on financial time series indicates that this is the case if one examines their properties from a statistical point of view: the seemingly random variations of asset prices do share some quite non-trivial statistical properties. Such properties, common across a wide range of instruments, markets and time periods are called stylized empirical fact s. Stylized facts are thus obtained by taking a common denominator among the properties observed in studies of different markets and instruments. Obviously by doing so one gains in generality but tends to lose in precision of the statements one can make about asset returns. Indeed, stylized facts are usually formulated in terms
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Autoregressive Conditional Heteroskedasticity (ARCH) Model 4 of qualitative properties of asset returns and may not be precise enough to distinguish among different parametric models.
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This note was uploaded on 01/11/2012 for the course ECO 601 taught by Professor Hakanyilmazkuday during the Fall '11 term at FIU.

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ARCH - AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY(ARCH...

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