Fractionally integrated generalized autoregressive conditional heteroskedasticity

Long-memory in an order-driven market

“…Several papers show that many financial time series are characterized by long memory processes. For example, long memory is detected in absolute returns of the S&P 500 ) and volatility of nominal exchange rates (Baillie, Bollerslev and Mikkelsen (1996)). …”

“…At a given point in time, investors look back at the past performance of their predictions. They realize their past mistakes on these predictions and update their prediction methods to new ones by imitating strategies 1 Long memory is detected in absolute returns of S&P 500 ) and volatility of nominal exchange rates (Baillie, Bollerslev and Mikkelsen (1996)). …”

Practical Issues in the Analysis of Univariate GARCH Models

“…To understand volatility clustering, consider the GARCH(1, 1) model in (7). Usually the GARCH coefficient b 1 is found to be around 0.9 for many daily or weekly financial time series.…”

“…The modified Ljung-Box statistic (12) can be used to test the null of no autocorrelation up to a specific lag, and Engle's LM statistic (13) can be used to test the null of no remaining ARCH effects 6 . If it is assumed that the errors are Gaussian, then a plot ofˆ t /σ t against time should have roughly ninety five percent of its values between ±2; a normal qq-plot ofˆ t /σ t should look roughly linear 7 ; and the JB statistic should not be too much larger than six. Table 3 gives model selection criteria for a variety of GARCH(p, q) fitted to the daily returns on Microsoft and the S&P 500.…”

An Introduction to Univariate GARCH Models

“…From (30) it is seen that the e¤ect of the lagged " 2 t on the conditional variance decays hyperbolically as a function of the lag length. This is the reason why Baillie, Bollerslev and Mikkelsen (1996) introduced the FIGARCH model, as it would conveniently explain the apparent slow decay in autocorrelation functions of squared observations of many daily return series. The FIGARCH model thus o¤ers a competing view to the one according to which changes in parameters in a GARCH model are the main cause of the slow decay in the autocorrelations.…”