Calculates and returns the (up/down) resampled time series.

## Syntax

**RESAMPLE**(

**X**,

**Stock**,

**Sampling**,

**method**)

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

**Stock** is the univariate time series data corresponds to a Stock or flow type of variable.

**Sampling** is the new relative sampling rate; 1.0 = input date sampling rate, > 1.0 = Up-Sampling, < 1.0 = Down-Sampling.

**method** is the imputation method for finding intermediate observations values (0=None, 1=Forward Flat, 2=Backward Flat, 3=Linear, 4=Cubic Spline, 5=FFT, etc.).

Value | Method |
---|---|

0 | None |

1 | Forward Flat |

2 | Backward Flat |

3 | Linear (default) |

4 | Cubic Spline |

5 | Fast Fourier Transform |

## Remarks

- The time series is homogeneous or equally spaced.
- The time series does not include any missing value or spaces.
- Economics, business, accounting, and related fields often distinguish between quantities that are stocks and those that are flows. These differ in their units of measurement:
- A stock variable is measured at one specific time, and represents a quantity existing at that point in time (e.g. price, inventory, capital, liabilities, assets, etc.), which may have accumulated in the past.
- A flow variable is measured over an interval of time. Therefore a flow would be measured per unit of time (say a month) (e.g. sales, profit, income, investment, etc.).

- The imputation method is only needed if the relative sampling value creates an new observation. This is often the case with Up-sampling ( value > 1), or obscure down-sampling (e.g. 0.333, etc.)
- For time series of flow-type, the function converts (i.e. integrates) the input time series to a stock-type, resampls it, and, finally, converts (i.e. differences) the resultant (new) time series to a flow-type.
- The value of the first observation in the output time series is either estimated for up-sampling cases, or ommitted (i.e. misisng value) for down-sampling cases.
- The time index of resampled time series is defined as follow:

$$ t^* = i \times f_r$$

where:- $0 \leq i \lt N^* $
- $t^*$ : is the time index of the new (resampled) time series.
- $N^*$ : is the new size of the resampled time series
- $f_r$ : is the relative sampling frequency

- The size of the returned array depends on the size as the input time series and the desired sampling rate.

$$ N^* = \lfloor (N-1) \times f_r +1 \rfloor$$

where:- $N$ : is the size of the input (original) time series
- $N^*$ : is the new size of the resampled time series
- $\lfloor.\rfloor$ : is the floor operator or function
- $f_r$ : is the relative sampling frequency

- The RESAMPLE function is available starting with version 1.64 TURRET.

## 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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