Forecasting the conditional variance of a process is primarily of interest if the conditional variance is changing over time.1 For a large number of financial time-series, as well as some macroeconomic time-series (such as inflation), time-varying conditional variances are an important feature. The autoregressive conditional heteroskedasticity (ARCH) model of Engle (1982), and its generalizations,2 have become almost indispensable in the modelling of financial series. ARCH models are capable of capturing variances that change (giving rise to clusterings of large (small) changes in the series), as well as other features typical of many financial series, such as thick-tailed unconditional distributions. As an example, Figure 3.1 plots monthly observations on three-month US Treasury Bill interest rates and ten-year Treasury bond interest rates (taken from the Federal Reserve of St Louis database, http://www.stls.frb.org/fred) and the first differences of these series. The clustering of large and small changes is clearly evident.
KeywordsCovariance Autocorrelation Volatility
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