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ACFTest
Calculates the p value of the statistical significance test for the population autocorrelation function.
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. 0=no lag, 1=1st lag, etc.). If missing, the default lag order of one (i.e. Lag=1) is assumed.
Method
is the calculation method for estimating the autocorrelation.
Value  Method 

0  Sample autocorrelation method.(default) 
1  Periodogrambased estimate. 
2  Crosscorrelation method 
rho
is the assumed autocorrelation function value. If missing, the default of zero is assumed.
Remarks
 The time series is homogeneous or equally spaced.
 The time series may include missing values (e.g. #N/A) at either end.
 The lag order (k) must be less than the time series size, or an error value (#VALUE!) is returned.
 The test hypothesis for the population autocorrelation:
Where:
 is the null hypothesis^{i}.
 is the alternate hypothesis.
 is the assumed population autocorrelation function for lag k.
 is the lag order.

Assuming a normal distributed population, the sample autocorrelation has a normal distribution:
Where:
 is the sample autocorrelation for lag k.
 is the population autocorrelation for lag k.
 is the standard deviation of the sample autocorrelation function for lag k.

The variance of the sample autocorrelation is computed as:
Where:
 is the standard error of the sample autocorrelation for lag k.
 is the sample data size.
 is the sample autocorrelation function for lag j.
 is the lag order.
 This is a twosides (i.e. twotails) test, so the computed pvalue should be compared with half of the significance level ().
Examples
Example 1: In this example, we use the autocorrelation test function (ACFTest) to examine the significance of the sample autocorrelation of the second lagorder.
A  B  

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

=ACF($B$2:$B$30,1,2)  Autocorrelation of order 2 (0.008)  
=ACFTest($B$2:$B$30,1,2,0)  pvalue of ACF(2) test when ACF(2) = 0 (0.483) 
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