# TSSUB - Time Series Subtraction

Returns an array of the difference between two time series.

## Syntax

TSSUB(X, Y)
X
is the first univariate time series data (a one dimensional array of cells (e.g. rows or columns)).
Y
is the second univariate time series data. If a single value is passed, it will be subtracted from all observations in the first time series.

## Remarks

1. The time series are homogeneous or equally spaced.
2. The two time series have an identical number of observations and time order, or the second series contains a single value.
3. In the case where the two time series are identically sized, the second series is subtracted from the first point-by-point:
$$\left[z_t\right] = \left[x_t\right] - \left[y_t\right]$$
Where:
• $\left[z_t\right]$ is the difference time series.
• $\left[x_t\right]$ is the first time series.
• $\left[y_t\right]$ is the second time series.
4. In the case where the second time series is passed as a single value ($\alpha$), this constant is subtracted from all points in the first time series:
$$\left[z_t\right] =\left[x_t\right] - \left[\alpha\right]$$
Where:
• $\left[z_t\right]$ is the difference time series.
• $\left[x_t\right]$ is the first time series.
• $\alpha$ is a constant value.
5. The returned array has the same size and time order as the first input time series.

## References

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