EWMA

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)).

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 1 is assumed.

1. The time series is homogeneous or equally spaced.
2. The time series may include missing values (e.g. #N/A) at either end.
3. The EWMA function assumes that the time series has an average equal to zero.
4. The exponential-weighted moving average is calculated as:
   

   Where:

   • is the value of the time series value at time t.
   • is the smoothing parameter (i.e. a non-negative constant between 0 and 1).
5. The size of the EWMA 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).

Example 1:

See the attached spreadsheet file

The plot of the EWMA with the original data is shown below:

• Hull, John C.; Options, Futures and Other DerivativesFinancial 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