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# EWXCF

Computes the correlation factor using the exponential-weighted correlation function (i.e. using the exponential-weighted covariance (EWCOV) and volatility (EWMA^{i}/EWV^{i}) method).

## Syntax

**EWXCF**(

^{i}**X**,

**Y**,

**Order**,

**Lambda**,

**T**)

**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 (a one dimensional array of cells (e.g. rows or columns)).

**Order**

is the time order in the data series (i.e. whether the first data point corresponds to the earliest or latest date (earliest date=1 (default), latest date=0)).

Order | Description |
---|---|

1 | ascending (the first data point corresponds to the earliest date) (default) |

0 | descending (the first data point corresponds to the latest date) |

**Lambda**

is the smoothing parameter used for the exponential-weighting scheme. If missing, the default value of 0.94 is assumed.

**T**

is the forecast time/horizon (expressed in terms of steps beyond the end of the time series X). If missing, the default value of 1 is assumed.

## Remarks

- The time series is homogeneous or equally spaced.
- The two time series must have identical size and time order.
- The correlation is defined as:

Where:

- is the sample correlation between X and Y at time t.
- is the sample exponential-weighted covariance between X and Y at time t.
- is the sample exponential-weighted volatility for the time series X at time t.
- is the sample exponential-weighted volatility for the time series Y at time t.
- is the smoothing factor used in the exponential-weighted volatility and covariance calculations.

- If the input data sets do not have a zero mean, the
**EWXCF**Excel function removes the mean from each sample data on your behalf. - The
**EWXCF**uses the EWMA volatility and EWCOV representations which do not assume a long-run average volatility (or covariance), and thus, for any forecast horizon beyond one-step, the EWXCF returns a constant value.

## Examples

## References

- Hull, John C.; Options, Futures and Other Derivatives Financial Times/ Prentice Hall (2003),pp 385-387, ISBN 1-405-886145
- 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