What is Periodicity analysis?

Periodicity analysis is the mining of periodic patterns, namely, the search for recurring patterns in time-related series data. Periodicity analysis can be used in several important areas. For example, seasons, tides, planet trajectories, daily power consumptions, daily traffic patterns, and weekly TV programs all present certain periodic patterns.

Periodicity analysis is implemented over time-series data, which includes sequences of values or events generally measured at equal time intervals (e.g., hourly, daily, weekly). It can also be applied to other time-related sequence data where the value or event may occur at a non-equal time interval or at any time (e.g., online transactions). Furthermore, the elements to be analyzed can be numerical data, including daily temperature or power consumption fluctuations, or categorical records (events), including buying a product or watching a game.

The issues of mining periodic patterns can be considered from several perspectives. It depends on the coverage of the pattern, and it can classify periodic patterns into full versus partial periodic patterns −

A full periodic pattern is a pattern where every point in time contributes (precisely or approximately) to the cyclic behavior of a time-related sequence. For example, all of the days in the year approximately contribute to the seasonal cycle of the year.

A partial periodic pattern specifies the periodic behavior of a time-related sequence at some but not all of the points in time. For instance, Sandy reads the New York Times from 7:00 to 7:30 every weekday morning, but its activities at other times do not have much regularity. Partial periodicity is a looser form of periodicity than full periodicity and occurs more commonly in the real world.

It is based on the precision of the periodicity, a pattern can be either synchronous or asynchronous, where the former requires that an event occurs at a relatively fixed offset in each “stable” period, such as 3 p.m. every day, whereas the latter allows that the event fluctuates in a somewhat loosely defined period.

A pattern can also be either precise or approximate, depending on the data value or the offset within a period. For example, if Sandy reads the newspaper at 7:00 on multiple days, but at 7:10 or 7:15 on others, this is a suitable periodic pattern.