+=head1 Aberrant Behavior Detection with Holt-Winters Forecasting
+
+In addition to the aggregate functions, there are a set of specialized
+functions that enable B<RRDtool> to provide data smoothing (via the
+Holt-Winters forecasting algorithm), confidence bands, and the flagging
+aberrant behavior in the data source time series:
+
+=over
+
+=item *
+
+B<RRA:>I<HWPREDICT>B<:>I<rows>B<:>I<alpha>B<:>I<beta>B<:>I<seasonal period>B<:>I<rra-num>
+
+=item *
+
+B<RRA:>I<SEASONAL>B<:>I<seasonal period>B<:>I<gamma>B<:>I<rra-num>
+
+=item *
+
+B<RRA:>I<DEVSEASONAL>B<:>I<seasonal period>B<:>I<gamma>B<:>I<rra-num>
+
+=item *
+
+B<RRA:>I<DEVPREDICT>B<:>I<rows>B<:>I<rra-num>
+
+=item *
+
+B<RRA:>I<FAILURES>B<:>I<rows>B<:>I<threshold>B<:>I<window length>B<:>I<rra-num>
+
+=back
+
+These B<RRAs> differ from the true consolidation functions in several ways.
+First, each of the B<RRA>s is updated once for every primary data point.
+Second, these B<RRAs> are interdependent. To generate real-time confidence
+bounds, then a matched set of HWPREDICT, SEASONAL, DEVSEASONAL, and
+DEVPREDICT must exist. Generating smoothed values of the primary data points
+requires both a HWPREDICT B<RRA> and SEASONAL B<RRA>. Aberrant behavior
+detection requires FAILURES, HWPREDICT, DEVSEASONAL, and SEASONAL.
+
+The actual predicted, or smoothed, values are stored in the HWPREDICT
+B<RRA>. The predicted deviations are store in DEVPREDICT (think a standard
+deviation which can be scaled to yield a confidence band). The FAILURES
+B<RRA> stores binary indicators. A 1 marks the indexed observation a
+failure; that is, the number of confidence bounds violations in the
+preceding window of observations met or exceeded a specified threshold. An
+example of using these B<RRAs> to graph confidence bounds and failures
+appears in L<rrdgraph>.
+
+The SEASONAL and DEVSEASONAL B<RRAs> store the seasonal coefficients for the
+Holt-Winters forecasting algorithm and the seasonal deviations respectively.
+There is one entry per observation time point in the seasonal cycle. For
+example, if primary data points are generated every five minutes, and the
+seasonal cycle is 1 day, both SEASONAL and DEVSEASONAL with have 288 rows.
+
+In order to simplify the creation for the novice user, in addition to
+supporting explicit creation the HWPREDICT, SEASONAL, DEVPREDICT,
+DEVSEASONAL, and FAILURES B<RRAs>, the B<RRDtool> create command supports
+implicit creation of the other four when HWPREDICT is specified alone and
+the final argument I<rra-num> is omitted.
+
+I<rows> specifies the length of the B<RRA> prior to wrap around. Remember
+that there is a one-to-one correspondence between primary data points and
+entries in these RRAs. For the HWPREDICT CF, I<rows> should be larger than
+the I<seasonal period>. If the DEVPREDICT B<RRA> is implicitly created, the
+default number of rows is the same as the HWPREDICT I<rows> argument. If the
+FAILURES B<RRA> is implicitly created, I<rows> will be set to the I<seasonal
+period> argument of the HWPREDICT B<RRA>. Of course, the B<RRDtool>
+I<resize> command is available if these defaults are not sufficient and the
+create wishes to avoid explicit creations of the other specialized function
+B<RRAs>.
+
+I<seasonal period> specifies the number of primary data points in a seasonal
+cycle. If SEASONAL and DEVSEASONAL are implicitly created, this argument for
+those B<RRAs> is set automatically to the value specified by HWPREDICT. If
+they are explicitly created, the creator should verify that all three
+I<seasonal period> arguments agree.
+
+I<alpha> is the adaption parameter of the intercept (or baseline)
+coefficient in the Holt-Winters forecasting algorithm. See L<rrdtool> for a
+description of this algorithm. I<alpha> must lie between 0 and 1. A value
+closer to 1 means that more recent observations carry greater weight in
+predicting the baseline component of the forecast. A value closer to 0 mean
+that past history carries greater weight in predicted the baseline
+component.
+
+I<beta> is the adaption parameter of the slope (or linear trend) coefficient
+in the Holt-Winters forecasting algorithm. I<beta> must lie between 0 and 1
+and plays the same role as I<alpha> with respect to the predicted linear
+trend.
+
+I<gamma> is the adaption parameter of the seasonal coefficients in the
+Holt-Winters forecasting algorithm (HWPREDICT) or the adaption parameter in
+the exponential smoothing update of the seasonal deviations. It must lie
+between 0 and 1. If the SEASONAL and DEVSEASONAL B<RRAs> are created
+implicitly, they will both have the same value for I<gamma>: the value
+specified for the HWPREDICT I<alpha> argument. Note that because there is
+one seasonal coefficient (or deviation) for each time point during the
+seasonal cycle, the adaptation rate is much slower than the baseline. Each
+seasonal coefficient is only updated (or adapts) when the observed value
+occurs at the offset in the seasonal cycle corresponding to that
+coefficient.
+
+If SEASONAL and DEVSEASONAL B<RRAs> are created explicitly, I<gamma> need not
+be the same for both. Note that I<gamma> can also be changed via the
+B<RRDtool> I<tune> command.
+
+I<rra-num> provides the links between related B<RRAs>. If HWPREDICT is
+specified alone and the other B<RRAs> created implicitly, then there is no
+need to worry about this argument. If B<RRAs> are created explicitly, then
+pay careful attention to this argument. For each B<RRA> which includes this
+argument, there is a dependency between that B<RRA> and another B<RRA>. The
+I<rra-num> argument is the 1-based index in the order of B<RRA> creation
+(that is, the order they appear in the I<create> command). The dependent
+B<RRA> for each B<RRA> requiring the I<rra-num> argument is listed here:
+
+=over
+
+=item *
+
+HWPREDICT I<rra-num> is the index of the SEASONAL B<RRA>.
+
+=item *
+
+SEASONAL I<rra-num> is the index of the HWPREDICT B<RRA>.
+
+=item *
+
+DEVPREDICT I<rra-num> is the index of the DEVSEASONAL B<RRA>.
+
+=item *
+
+DEVSEASONAL I<rra-num> is the index of the HWPREDICT B<RRA>.
+
+=item *
+
+FAILURES I<rra-num> is the index of the DEVSEASONAL B<RRA>.
+
+=back
+
+I<threshold> is the minimum number of violations (observed values outside
+the confidence bounds) within a window that constitutes a failure. If the
+FAILURES B<RRA> is implicitly created, the default value is 7.
+
+I<window length> is the number of time points in the window. Specify an
+integer greater than or equal to the threshold and less than or equal to 28.
+The time interval this window represents depends on the interval between
+primary data points. If the FAILURES B<RRA> is implicitly created, the
+default value is 9.
+