First order pivot points are defined as 3 or 5 bar "V" shaped patterns. For example a high with a lower high either side of the peak and in the case of the 5 bar variant with lower highs adjacent to a high below the peak.
Second order pivot points are defined by three first order pivots in the same manner. For example a peak pivot high with a lower pivot high to either side.
Third order pivots follow the same pattern, a peak second order pivot high with two adjacent second order pivot highs.

As it can take a significant and variable amount of time before higher order pivots are confirmed, it is generally inadvisable to use higher order pivots for live trading!
However they can be used for historical analysis. For example to delineate market structure of major market inflections.

For example :

snapshot
Delineating market structure using 2nd order pivots derived from 3 bar, 1st order pivots


snapshot
Major market inflections from 3rd order pivots derived from 5 bar, 1st order pivots
Pivot PointsTrend Analysis

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