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Posted 07-25-2021 08:04 AM
(771 views)

hi, i am quite new with SAS and i am struggling to understand the ADF process for selecting the correct number of lags

As a first step for the ADF test i tried to identify the correct number of lags that i have to include. I use monthly data, therefore i added ADF=12 lags and run the below code :

***ADF test***;

PROC ARIMA DATA= rethouse_reg1 ;

IDENTIFY VAR = DEPPC_forc STATIONARITY=(ADF=12) ;

RUN;

QUIT;

then i looked at the ADF and Trend Correlation analysis :

i looked at the trend and correlation analysis graph (see below). My series doesn't have trend (based on the graph) and has mean different than zero (based on table below mean = 6.381432) therefore, i concluded that i have to use the __ single mean__ in ADF.

After this i looked at the ADF table (see at the bottom) in the single mean model and starting from the bottom (12 lags) I found that the 9 lags are statistical significant (0.0146<0.05). __Based on this i concluded that i have to use 9 lags in the ADF test. __

Then i looked at the ACF graph and counted the number of columns which are outside the shed blue area and found __11lags __and i understood that i had to include 11lags for the ADF (compare to 9lags that found earlier)

my questions are :

1) Is the steps that i followed correct for selecting the appropriate number of lags for the ADF?

2) If yes, which one of the above results for the correct number of lags i can trust and include in my ADF test and why?

Name of Variable = DEPPC_forc | |

Mean of Working Series | 6.381432 |

Standard Deviation | 2.35614 |

Number of Observations | 277 |

ugmented Dickey-Fuller Unit Root Tests | |||||||

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

Zero Mean | 0 | 0.4318 | 0.7889 | 0.37 | 0.792 | ||

1 | 0.3733 | 0.7738 | 0.3 | 0.7728 | |||

2 | -0.0458 | 0.6719 | -0.03 | 0.6726 | |||

3 | -0.5249 | 0.5642 | -0.3 | 0.5756 | |||

4 | -0.6041 | 0.5474 | -0.34 | 0.5629 | |||

5 | -0.595 | 0.5493 | -0.33 | 0.564 | |||

6 | -0.6329 | 0.5414 | -0.34 | 0.561 | |||

7 | -0.8189 | 0.5049 | -0.42 | 0.5322 | |||

8 | -1.4697 | 0.3989 | -0.65 | 0.4358 | |||

9 | -1.5907 | 0.3821 | -0.68 | 0.422 | |||

10 | -0.8402 | 0.5009 | -0.43 | 0.5252 | |||

11 | -0.5906 | 0.5502 | -0.33 | 0.5657 | |||

12 | -0.145 | 0.6494 | -0.12 | 0.641 | |||

Single Mean | 0 | -2.7088 | 0.6911 | -0.81 | 0.8142 | 0.57 | 0.9306 |

1 | -3.6673 | 0.5752 | -1.01 | 0.7512 | 0.74 | 0.8816 | |

2 | -8.616 | 0.1846 | -1.81 | 0.3773 | 1.82 | 0.6057 | |

3 | -12.848 | 0.0651 | -2.2 | 0.2058 | 2.52 | 0.4246 | |

4 | -15.2504 | 0.0354 | -2.34 | 0.1595 | 2.84 | 0.3433 | |

5 | -15.8331 | 0.0305 | -2.33 | 0.1647 | 2.79 | 0.3552 | |

6 | -19.2865 | 0.0127 | -2.49 | 0.1191 | 3.21 | 0.2497 | |

7 | -25.4427 | 0.0028 | -2.72 | 0.0731 | 3.78 | 0.1015 | |

8 | -45.8484 | 0.0015 | -3.18 | 0.0228 | 5.1 | 0.0347 | |

9 | -64.8018 | 0.0015 | -3.34 | 0.0146 |
5.61 | 0.0205 | |

10 | -35.3822 | 0.0015 | -2.8 | 0.0601 | 4 | 0.0875 | |

11 | -29.8813 | 0.0015 | -2.61 | 0.0917 | 3.51 | 0.1724 | |

12 | -9.0271 | 0.1669 | -1.7 | 0.4324 | 1.5 | 0.6861 | |

Trend | 0 | -1.8741 | 0.9729 | -0.55 | 0.9808 | 0.95 | 0.9735 |

1 | -2.8408 | 0.9428 | -0.76 | 0.9668 | 0.89 | 0.9788 | |

2 | -8.555 | 0.5357 | -1.72 | 0.7411 | 1.62 | 0.8528 | |

3 | -13.339 | 0.2423 | -2.14 | 0.5208 | 2.43 | 0.6899 | |

4 | -16.6115 | 0.1298 | -2.32 | 0.423 | 2.8 | 0.6158 | |

5 | -17.441 | 0.1099 | -2.29 | 0.4385 | 2.76 | 0.6237 | |

6 | -23.2314 | 0.0324 | -2.53 | 0.3138 | 3.29 | 0.5173 | |

7 | -34.3311 | 0.0025 | -2.82 | 0.1909 | 4.05 | 0.3633 | |

8 | -82.3673 | 0.0006 | -3.35 | 0.0604 | 5.71 | 0.0814 | |

9 | -210.116 | 0.0001 | -3.58 | 0.0332 | 6.51 | 0.0441 | |

10 | -70.2109 | 0.0006 | -2.99 | 0.136 | 4.58 | 0.2574 | |

11 | -59.658 | 0.0006 | -2.82 | 0.1932 | 4.05 | 0.3632 | |

12 | -10.7044 | 0.3831 | -1.6 | 0.7915 | 1.48 | 0.8809 |

2 REPLIES 2

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Hello,

I do not master the peculiarities and intricacies of the ADF test anymore. I did, but I haven't used it since a long time.

It takes a while before you can fluently use it (in my case at least).

However, I think this paper may help you out :

Paper 3294-2015

An Introduction to Testing for Unit Roots Using SAS®:

The Case of U.S. National Health Expenditures

Donald McCarthy, Department of Research and Evaluation, Kaiser Permanente

https://support.sas.com/resources/papers/proceedings15/3294-2015.pdf

There are 10 occurrences of 'lag length' in the paper and a macro that implements the Ng and Perron (2001) approach.

Ng, S and P. Perron. 2001. “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power.” Econometrica, Vol. 69, No. 6: 1519–1554.

There's also a a rule of thumb based on the number of observations in the sample.

Good luck,

Koen

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hi there, thank you. i am going to have a look at this. I have searched on google and to be honest there is no one clear guidance on the steps that have to be followed (or it is not clear to me). The same happens with the ADF approach. Many people try to explain but they miss to provide crucial details. Anyway, i am going to have a look. thanks again

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