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) (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, 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.

## Files Examples

## Related Links

## 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.

## Comments

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