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ADFTest
Returns the pvalue of the Augmented DickeyFuller Test in Excel (ADF^{i}), which tests for a unit root in the time series sample.
Syntax
X
is the univariate time series data (one dimensional array of cells (e.g. rows or columns)).
Order
is the time order of the data series (i.e. the first data point's corresponding 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) 
Length
is the lag^{i} length of the autoregressive process. If missing, an initial value equal to the cubic root of the input data size is used.
Options
are the model description flags for the Dickey Fuller test variant (1 = no constant, 2 = contantonly, 3 = constant and trend, 4 = constant, trend, and trend squared).
Method  Description 

1  no deterministic components 
2  constant only 
3  trend only 
4  constant and trend 
5  constant, trend, and trend squared 
testdown
is the mode of testing. If set to TRUE (default), ADFTest performs a series of tests; it starts with the input length lag, but the actual length lag order used is obtained by testing down.
Return_type
is a switch to select the return output (1 = PValue (default), 2 = Test Stats, 3 = Critical Value.
Method  Description 

1  PValue 
2  Test Statistics (e.g. Zscore) 
3  Critical Value 
Alpha
is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Remarks

The testing procedure for the ADF test is applied to the following model:
(1) Where:
 is the first different operator
 is a constant
 is the coefficient on a time trend
 is the coefficient on a squared time trend
 This model can be estimated, and testing for a unit root is equivalent to testing that .
 In sum, the Augmented DickeyFuller Test in Excel test hypothesis is as follows:
Where:
 is the null hypothesis (i.e. has a unitroot)
 is the alternate hypothesis (i.e. does not have a unitroot)
 The test statistics () value is calculated as follows:
where:
 is the estimated coefficient
 is the standard error in the coefficient estimate
 The test statistics value () is compared to the relevant critical value for the Dickeyâ€“Fuller Test. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that no unitroot is present.
 The ADFTest does not directly test for stationarity, but indirectly through the existence (or absence) of a unitroot. Furthermore, Augmented DickeyFuller Test in Excel incorporates a deterministic trend (and trend squared), so it allows a trendstationary process to occur.
 The main difference between the ADFTest and a normal Dickey Fuller test is that ADFTest allows for higherorder autoregressive processes.
 For the testdown approach, we start with a given maximum lag length and test down by running several tests; in each, we exaimine the highorder coefficient's tstat for significance.
 It is not possible to use a standard tdistribution to provide critical values for this test. Therefore this test statistic (i.e. ) has a specific distribution simply known as the Dickeyâ€“Fuller table.
 The time series must have at least 10, and no more than 10,000 nonmissing observations.
 The time series is homogeneous or equally spaced.
 The time series may include missing values (e.g. #N/A) at either end.
Examples
Example 1:
A  B  

1  Date  Data 
2  January 10, 2008  2.827 
3  January 11, 2008  0.947 
4  January 12, 2008  0.877 
5  January 14, 2008  1.209 
6  January 13, 2008  1.669 
7  January 15, 2008  0.835 
8  January 16, 2008  0.266 
9  January 17, 2008  1.361 
10  January 18, 2008  0.343 
11  January 19, 2008  0.475 
12  January 20, 2008  1.153 
13  January 21, 2008  1.144 
14  January 22, 2008  1.070 
15  January 23, 2008  1.491 
16  January 24, 2008  0.686 
17  January 25, 2008  0.975 
18  January 26, 2008  1.316 
19  January 27, 2008  0.125 
20  January 28, 2008  0.712 
21  January 29, 2008  1.530 
22  January 30, 2008  0.918 
23  January 31, 2008  0.365 
24  February 1, 2008  0.997 
25  February 2, 2008  0.360 
26  February 3, 2008  1.347 
27  February 4, 2008  1.339 
28  February 5, 2008  0.481 
29  February 6, 2008  1.270 
30  February 7, 2008  1.710 
31  February 8, 2008  0.125 
32  February 9, 2008  0.940 
Formula  Description (Result)  

=ADFTest($B$2:$B$32,1,,1,TRUE,1)  PValue with no Constant (0.01)  
=ADFTest ($B$2:$B$32,1,,2,TRUE,2)  Test Stats with Constant Only (8.784)  
ADFTest ($B$2:$B$32,1,,3,TRUE,3)  Critical Value with Constant and Trend (3.966)  
ADFTest ($B$2:$B$32,1,,4,TRUE,1)  PValue with Constant, Trend, and Trend Squared (0.01) 
Examples
References
 Jarque, Carlos M.; Anil K. Bera (1980). "Efficient tests for normality, homoscedasticity and serial independence of regression residuals". Economics Letters 6 (3): 255259.
 Ljung, G. M. and Box, G. E. P., "On a measure of lack of fit in time series models." Biometrika 65 (1978): 297303
 Enders, W., "Applied econometric time series", John Wiley & Sons, 1995, p. 8687
 Shapiro, S. S. and Wilk, M. B. (1965). "An analysis of variance test for normality (complete samples)", Biometrika, 52, 3 and 4, pages 591611