Calculates the estimated value of the **exponentially weighted moving average (EWMA)** (aka exponentially weighted volatility (EWV).

## Syntax

**EWMA Excel**(

**X**,

**Order**,

**Lambda**,

**T**)

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

**Order**is the time order of 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) |

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

**Lambda** is the smoothing parameter used for the exponential-weighting scheme. If missing, a 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, a default value of 0 is assumed.

## Remarks

- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- If the input data set does not have a zero mean, the
**EWMA Excel**function removes the mean from your sample data on your behalf. - The
**exponentially weighted moving average**(\sigma_t) is calculated as:

$$\sigma_t^2=\lambda \sigma_{t-1}^2+(1-\lambda)x_{t-1}^2$$

Where:

- $x_t$ is the value of the time series value at time t.
- $\lambda$ is the smoothing parameter (i.e. a non-negative constant between 0 and 1).

- The size of the
**EWMA Excel**time series is equal to the input time series, but with the first observation (or last, if the original series is reversed) set to missing (i.e. #N/A). - The
**EWMA**volatility representation does not assume a long-run average volatility, and thus, for any forecast horizon beyond one-step, the EWMA returns a constant value.

## Examples

### Example 1:

*See the attached spreadsheet file*

The **EWMA** Excel plot with the original data is shown below:

## References

- Hull, John C.; Options, Futures and Other Derivatives Financial Times/ Prentice Hall (2003),pp 372-374, 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

## 0 Comments