ACF (Pro.)

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. 0=no lag, 1=1st lag, etc.). If missing, the default lag order of one (i.e. Lag=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 lag order (k) must be less than the time series size, or else an error value (#VALUE!) is returned.
4. The ACF values are bound between -1 and 1, inclusive.
5. The sample autocorrelation is computed as:

   Where:

   • is the value of the time series at time t.
   • is the lag order.
   • is the number of non-missing values in the time series data.
   • is the sample average/mean of the time series.
6. Special Cases:
   • By definition,

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 - Autocorrelation function (ACF)