Returns the time-reversed order time series (i.e. the first observation is swapped with the last observation, etc.): both missing and non-missing values.

## Syntax

**REVERSE**(

**X**)

**X** is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).

## Remarks

- The time series is homogeneous or equally spaced.
- The reverse operator changes the time-order from ascending to descending or vice versa:

$$ \left[z_t\right] = \left[x_{T-t}\right] $$

Where:

- $ \left[z_t\right]$ is the reversed time series.
- $\left[x_t\right]$ is the input time series.
- $T$ is the number of observations (including missing values) in the input time series.

- The returned array has the same size as the input time series.

## Files Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

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