reading results of Augmented Dickey-Fuller Unit Root Test

[#1]

Dear fellows:
With ARIMA procedure, I can carry out Augmented Dickey-Fuller Unit Root Test. However, I do not understand 'rho' in test output and I can not find any related information in sas documents or statistical books/literatures.

I assume that 'rho' is coefficient on 1st lag and has range [-1,1]; and I assume that unit root test is to find out 'rho' equal to 1 or not. For instance, Y(t) = ...+'rho'Y(t-1)+... However, in my test results, I get 'rho' value as big as 50.
Would you please do me a favor and explain what 'rho' means here?
Many thanks.
My e-mail is as follow:

yunfei.zhao@email.wsu.edu

Yunfei Zhao

[#2 · Accepted solution]

I asked a similar question and this is the response from JMP Technical Support:

Dear Mark,

Thank you for your question regarding ADF tests in JMP.

The values printed for the Zero Mean, Single Mean and Trend ADF in JMP are the Tau statistics associated with the Dickey-Fuller test. Because Dickey and Fuller produced look-up tables for the critical values associated with the distribution of the Tau statistic, and because the associated p-values would only be approximations, the developer decided not to print approximate p-values for these statistics. Tabled values may be found in the following references:

Dickey, D. A. and Fuller, W. A. (1979), "Distribution of the Estimation for Autoregressive Time Series with a Unit Root," Journal of the American Statistical Association, 74, 427-431.

Dickey, D. A., Hasza, D. P., and Fuller, W. A. (1984), "Testing for Unit Roots in Seasonal Time Series," Journal of the American Statistical Association, 79, 355-367.

Another excellent reference for the Dickey-Fuller tests is:

Hamilton, J. D. (1994), Time Series Analysis, Princeton: Princeton University Press.

You may want to refer to the tables noted in the above references to determine the significance of the test statistics printed by JMP.

[#3]

You have to decide what model you test for. JMP gives you the statistics for all three models. The critical values are not provided by JMP (in version 10), but can be found in a simple Google search (see below). Check out this example also: ADF Augmented Dickey-Fuller Unit Root Test - YouTube:

Pasted from <http://akson.sgh.waw.pl/~mrubas/EP/TabliceStatystyczneDF.doc> :

Critical Values for the Dickey-Fuller

Unit Root t-Test Statistics

                        Probability to the Right of Critical Value

Model Statistic N   1%    2.5%    5%    10%    90%     95%   97.5%  99%

Model I (no constant, no trend)

       ADFtr   25  -2.66  -2.26  -1.95  -1.60   0.92   1.33   1.70   2.16

              50  -2.62  -2.25  -1.95  -1.61   0.91   1.31   1.66   2.08

             100  -2.60  -2.24  -1.95  -1.61   0.90   1.29   1.64   2.03

             250  -2.58  -2.23  -1.95  -1.61   0.89   1.29   1.63   2.01

             500  -2.58  -2.23  -1.95  -1.61   0.89   1.28   1.62   2.00

            >500  -2.58  -2.23  -1.95  -1.61   0.89   1.28   1.62   2.00

Model II (constant, no trend)

       ADFtr   25  -3.75  -3.33  -3.00  -2.62  -0.37   0.00   0.34   0.72

              50  -3.58  -3.22  -2.93  -2.60  -0.40  -0.03   0.29   0.66

             100  -3.51  -3.17  -2.89  -2.58  -0.42  -0.05   0.26   0.63

             250  -3.46  -3.14  -2.88  -2.57  -0.42  -0.06   0.24   0.62

             500  -3.44  -3.13  -2.87  -2.57  -0.43  -0.07   0.24   0.61

            >500  -3.43  -3.12  -2.86  -2.57  -0.44  -0.07   0.23   0.60

Model III (constant, trend)

       ADFtr   25  -4.38  -3.95  -3.60  -3.24  -1.14  -0.80  -0.50  -0.15

              50  -4.15  -3.80  -3.50  -3.18  -1.19  -0.87  -0.58  -0.24

             100  -4.04  -3.73  -3.45  -3.15  -1.22  -0.90  -0.62  -0.28

             250  -3.99  -3.69  -3.43  -3.13  -1.23  -0.92  -0.64  -0.31

             500  -3.98  -3.68  -3.42  -3.13  -1.24  -0.93  -0.65  -0.32

            >500  -3.96  -3.66  -3.41  -3.12  -1.25  -0.94  -0.66  -0.33