PACF (Pro.)

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)).

K
is the lag order (e.g. k=0 (no lag), k=1 (1st lag), etc.). If missing, the default of k=1 is assumed.

1. The time series is homogeneous or equally spaced.
2. ACF and PACF plots (i.e. correlograms) are tools commonly used for model identification in Box-Jenkins models.
3. PACF is the autocorrelation between and that is not accounted for by lags 1 to k-1, inclusive
4. Equivalently, PACF(k) is the ordinary least square (OLS) multiple-regression k-th coefficient ().

   Where:

   • is the input time series.
   • is the lag order.
   • is the j-th coefficient of the linear multiple regression (i.e. AR(j)).

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 - Partial auto correlation function (PACF)
• Wikipedia - Box-Jenkins methodology