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# 6.17 `return_time`

`return_time` may be used to find hidden periodicity in multivariate data, e.g. embedded time series data. It computes a histogram of return times. For any given reference point, `return_time` calculates the time span until the time series returns to that location in phase space (by means of nearest neighbors). A histogram of these time spans is computed. Strong peaks in this histogram might be a sign of periodicity in the data.

Syntax:

- `r = return_time(pointset, query_indices, k, max_time, exclude)`
- `r = return_time(atria, pointset, query_indices, k, max_time, exclude)`

Input arguments:

- `atria` - output of `nn_prepare` for pointset (optional) (cf. Section 6.13)
- `pointset` - a `N` by `D` double matrix containing the coordinates of the point set, organized as `N` points of dimension `D`
- `query_indices` - query points are taken out of the pointset, `query_indices` is a vector of length `R` which contains the indices of the query points (indices may vary from 1 to N)
- `k` - number of nearest neighbors to be determined
- `max_time` - integer scalar, gives an upper limit for return times that should be considered.
- `exclude` - in case the query points are taken out of the pointset, exclude specifies a range of indices which are omitted from search. For example if the index of the query point is 124 and exclude is set to 3, points with indices 121 to 127 are omitted from search. Using exclude = 0 means: exclude self-matches

Output arguments:

- `r` - vector of length max_time, containing the histogram of return times

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