ARCH uses a big window but weighted averages. That is, we’ll give more weight to recent information, less to those that happened a long time ago. You can estimate these weights using an econometric model.
In yellow is the 5-day moving average of the standard deviations. In red is the one-year standard deviation, and the green is a five-year standard deviation. If you give the same information to a GARCH program (generalized autoregressive conditional heteroskedasticity) such as MatLab it will calculate the best set of weights.
Another way to look at the same output is in terms of a confidence interval. Each day you can ask “How high or low do I expect the market to go?”
The GARCH bands are time-varying confidence intervals. For instance, at any one point in time you can say with confidence that the market isn’t going to be higher than the blue band or lower than the green band.
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For the transcript of the original presentation go to the FT Business School - NYU Stern School of Business site.