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. the first data point's corresponding date (earliest date=1 (default), latest date=0)).

K is the seasonal difference order (e.g. K=0 (no lag), S=1 (1st lag), etc.) If missing, the default value of one is assumed.

D is the number of repeated differencing (e.g. d=0 (none), d=1 (difference once), 2= (difference twice), etc.). If missing, the default value of one is assumed.

1. The DIFF operator is defined as follow :
   
   $$Y_t=\left(1-L^k\right)^d X_t$$
   
   Where:
   
   • $\left[y_t\right]$ is the difference time series.
   • $\left[x_t\right]$ is the input time series.
   • $L$ is the lag operator.
   • $k$ is the seasonality length.
   • $d$ is the difference order.
2. The size of the output differenced time series is equal to the input time series, but with the first $s \times d$ observations are set to missing (i.e. #N/A).
3. The seasonal difference order (i.e. k) must be non-negative and smaller than the time series size (i.e. T).
   
   $0 \leq k \leq T-1 $
4. The input time series is homogenous and equally spaced.
5. The time series may include missing values (e.g. #N/A) at either end.

Example 1:

Files Examples

Related Links

• Wikipedia - Difference Operator
• Wikipedia - Delta Operator

References

• D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
• James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
• Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740
• Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
• Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568