Sas stationarity test 방법 adf

i have a time series variable which i checked it for stationarity using ADF test and arima proc in SAS

proc arima data=&td19; identify var=interest_rate stationarity=(adf=4); run; quit;

Below is the ADF test and trend & correlation analysis

i started from the table from the bottom (trend model) and using the Tau compared it with 5% until to reject the null. i concluded that the series is stationary since 0.0315<0.05 zero mean model

However, when i see the ACF/PACF, based on my understanding, the series in not stationary. This is because the ACF decays slowly

My questions are : is this series stationary or not?

Sas stationarity test 방법 adf

Sas stationarity test 방법 adf

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                                       The SAS System      14:11 Thursday, October 6, 2013   1

                                      The ARIMA Procedure

                                Name of Variable = ln_G_S_Index

                     Period(s) of Differencing                           1
                     Mean of Working Series                       0.094293
                     Standard Deviation                           0.316757
                     Number of Observations                             15
                     Observation(s) eliminated by differencing           1


                                        Autocorrelations

 Lag    Covariance    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1      Std Error

   0      0.100335        1.00000    |                    |********************|             0
   1     0.0026693        0.02660    |          .         |*        .          |      0.258199
   2     -0.018517        -.18456    |          .     ****|         .          |      0.258382
   3      0.029440        0.29342    |         .          |******    .         |      0.267025

                                 "." marks two standard errors


                                    Inverse Autocorrelations

               Lag    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                 1       -0.14763    |          .      ***|         .          |
                 2        0.19526    |          .         |****     .          |
                 3       -0.27516    |          .   ******|         .          |


                                    Partial Autocorrelations

               Lag    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                 1        0.02660    |          .         |*        .          |
                 2       -0.18539    |          .     ****|         .          |
                 3        0.31522    |          .         |******   .          |


                               Phillips-Perron Unit Root Tests

              Type           Lags         Rho    Pr < Rho        Tau    Pr < Tau

              Zero Mean         0    -11.6883      0.0066      -3.23      0.0033
                                1    -11.4504      0.0074      -3.23      0.0034
              Single Mean       0    -13.7527      0.0129      -3.71      0.0171
                                1    -12.6667      0.0218      -3.76      0.0157
              Trend             0    -14.5288      0.0601      -3.25      0.1144
                                1    -13.1531      0.1022      -3.20      0.1239
                                        The SAS System      14:11 Thursday, October 6, 2013   2

                                      The ARIMA Procedure

                                Name of Variable = ln_G_S_Index

                     Period(s) of Differencing                           1
                     Mean of Working Series                       0.094293
                     Standard Deviation                           0.316757
                     Number of Observations                             15
                     Observation(s) eliminated by differencing           1


                                        Autocorrelations

 Lag    Covariance    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1      Std Error

   0      0.100335        1.00000    |                    |********************|             0
   1     0.0026693        0.02660    |          .         |*        .          |      0.258199
   2     -0.018517        -.18456    |          .     ****|         .          |      0.258382
   3      0.029440        0.29342    |         .          |******    .         |      0.267025

                                 "." marks two standard errors


                                    Inverse Autocorrelations

               Lag    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                 1       -0.14763    |          .      ***|         .          |
                 2        0.19526    |          .         |****     .          |
                 3       -0.27516    |          .   ******|         .          |


                                    Partial Autocorrelations

               Lag    Correlation    -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

                 1        0.02660    |          .         |*        .          |
                 2       -0.18539    |          .     ****|         .          |
                 3        0.31522    |          .         |******   .          |


                            Augmented Dickey-Fuller Unit Root Tests

    Type           Lags         Rho    Pr < Rho        Tau    Pr < Tau          F    Pr > F

    Zero Mean         0    -11.6883      0.0066      -3.23      0.0033
                      1    -12.4302      0.0041      -2.42      0.0197
    Single Mean       0    -13.7527      0.0129      -3.71      0.0171       6.91    0.0157
                      1    -25.2133      <.0001      -3.63      0.0214       6.59    0.0206
    Trend             0    -14.5288      0.0601      -3.25      0.1144       6.44    0.0799
                      1    -45.0252      <.0001      -3.20      0.1265       6.92    0.0622
                                        The SAS System      14:11 Thursday, October 6, 2013   3

chl

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asked Oct 28, 2013 at 5:34

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3

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Look at the ADF Unit Root Test section.

If your data is a random walk with drift, then it will be under the type 'Single Mean'.

For the ADF test, H0: Non-stationary Ha: Stationary

if P-value < 0.05, you reject the null hypo (H0) and conclude that data series is stationary. It should be as you already differenced the data once.

Under 'Pr < Rho' which stands for the P-value of your Rho (autocorrelation), it is 0.0129 and <0.0001 thus, we reject the null hypo and conclude that the data is stationary.

answered Nov 4, 2013 at 3:44

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How do you check stationarity in SAS?

proc arima data=b; identify var=u stationarity=(adf=0); run; identify var=u stationarity=(pp=0); run; quit; The first IDENTIFY statement performs the ADF unit root tests for u. The stationarity test results are shown in Output 7.8. 8.

How many lags should I use in ADF test?

If you have quarterly data, test up to 4 lags. If you have monthly data test up to 12 lags. If the ADF test comes up with a high tau value and a resulting low p-value, you can reject the null hypothesis that the variable is non-stationary.

Why ADF test is better than DF test?

The primary differentiator between the two tests is that the ADF is utilized for a larger and more complicated set of time series models. The augmented Dickey-Fuller statistic used in the ADF test is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root.

What is the difference between Dickey

The augmented dickey- fuller test is an extension of the dickey-fuller test, which removes autocorrelation from the series and then tests similar to the procedure of the dickey-fuller. When we make a model for forecasting purposes in time series analysis, we require a stationary time series for better prediction.