Phone: +1 (888) 4279486
+1 (312) 2573777
Contact Us
PACFCI
Returns the confidence interval limits (upper/lower) for the partial autocorrelation function (PACF^{i}).
Syntax
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)).
Order  Description 

1  ascending (the first data point corresponds to the earliest date) (default) 
0  descending (the first data point corresponds to the latest date) 
K
is the lag^{i} order (e.g. k=0 (no lag), k=1 (1st lag), etc.). If missing, the default of k=1 is assumed.
Alpha
is the statistical significance level (i.e. alpha). If missing, the default value of 5% is assumed.
UL
is a flag to specify whether an upper (ul=1), or lower (ul=0) confidence interval bound is desired.
Remarks
 The time series is homogeneous or equally spaced.
 The sample ACF and PACF plots (i.e. correlograms) are tools commonly used for model identification in BoxJenkins models.

The PACFCI function is calculated as:
Where:
 is the population partialautocorrelation function for lag k.
 is the number of nonmissing observations in the input time series.
 is the sample partialautocorrelation function for lag k.
 PACF is the autocorrelation between and that is not accounted for by lags 1 to k1, inclusive.

Equivalently, PACF(k) is the ordinary least square (OLS) multipleregression kth coefficient ().
Where:
 is the input time series.
 is the lag order.
 is the jth coefficient of the multiple regression (i.e. AR(j)).
Examples
Example 1:
A  B  

1  Date  Data 
2  January 10, 2008  0.30 
3  January 11, 2008  1.28 
4  January 12, 2008  0.24 
5  January 13, 2008  1.28 
6  January 14, 2008  1.20 
7  January 15, 2008  1.73 
8  January 16, 2008  2.18 
9  January 17, 2008  0.23 
10  January 18, 2008  1.10 
11  January 19, 2008  1.09 
12  January 20, 2008  0.69 
13  January 21, 2008  1.69 
14  January 22, 2008  1.85 
15  January 23, 2008  0.98 
16  January 24, 2008  0.77 
17  January 25, 2008  0.30 
18  January 26, 2008  1.28 
19  January 27, 2008  0.24 
20  January 28, 2008  1.28 
21  January 29, 2008  1.20 
22  January 30, 2008  1.73 
23  January 31, 2008  2.18 
24  February 1, 2008  0.23 
25  February 2, 2008  1.10 
26  February 3, 2008  1.09 
27  February 4, 2008  0.69 
28  February 5, 2008  1.69 
29  February 6, 2008  1.85 
30  February 7, 2008  0.98 
Formula  Description (Result)  

=PACF($B$2:$B$30,1,1)  Partial autocorrelation of order 1 (0.236)  
=PACFCI($B$2:$B$30,1,1,5%,1)  Upper confidence interval for PACF of order 1 (0.364)  
=PACFCI($B$2:$B$30,1,1,5%,0)  Lower confidence interval for PACF of order 1 (0.364) 
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740