DIFF

X
is the 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)).

K
is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.). If missing, the default value of one 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 lag order (i.e. k) must be non-negative and smaller than the time series size.

   

4. The size of the differenced time series is equal to the input time series, but with the first k observations (or last, if the original series is reversed) set to missing (i.e. #N/A).
5. The differenced time series is:
   

   Where:

   • is the difference time series.
   • is the input time series.
   • is the lag operatorⁱ.
   • is the lag order.

Example 1:

• 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

• Wikipedia - Difference Operator
• Wikipedia - Delta Operator