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03-20-2014 03:13 PM

In the SAS documntation below taken from PROC VARMAX, tab "Getting started", section VECM, it says that "You can see that both series have unit roots.". I dont see this because variable y2 (for the trend model) is significant for both the rho(col 4) and tau(col 6) statistics, hence rejecting the null of unit root being present. Doesn't this mean that y2 is stationary? Please let me know your thoughts!

Thanks,

Prem

Figure 36.13: Dickey-Fuller Tests and Cointegration Rank Test

The VARMAX Procedure

y1 | Zero Mean | 1.47 | 0.9628 | 1.65 | 0.9755 |
---|---|---|---|---|---|

Single Mean | -0.80 | 0.9016 | -0.47 | 0.8916 | |

Trend | -10.88 | 0.3573 | -2.20 | 0.4815 | |

y2 | Zero Mean | -0.05 | 0.6692 | -0.03 | 0.6707 |

Single Mean | -6.03 | 0.3358 | -1.72 | 0.4204 | |

Trend | -50.49 | 0.0003 | -4.92 | 0.0006 |

In Dickey-Fuller tests, the second column specifies three types of models,

which are zero mean, single mean, or trend. The third column ( Rho ) and the

fifth column ( Tau ) are the test statistics for unit root testing. Other

columns are their -values. You can see that both series have unit roots. For a

description of Dickey-Fuller tests, see the section PROBDF Function for Dickey-Fuller Tests in

Chapter 5: SAS Macros and

Functions.

which are zero mean, single mean, or trend. The third column ( Rho ) and the

fifth column ( Tau ) are the test statistics for unit root testing. Other

columns are their -values. You can see that both series have unit roots. For a

description of Dickey-Fuller tests, see the section PROBDF Function for Dickey-Fuller Tests in

Chapter 5: SAS Macros and

Functions.

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03-21-2014 09:20 AM

I believe that the null hypothesis is that the series is an order 0 (no unit roots) and the alternative hypothesis is that it is order > 0 (1 or more unit roots).

So the significance rejects there NOT being a unit root.

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03-21-2014 06:48 PM

Thanks Chris.

I looked up a text which says that the null is "has unit root". Even if the null were "has no unit root", there is a discrepancy because either y1 or y2 is stationary because one of them is significant while the other isn't, whereas the documentation says both have unit roots.

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03-21-2014 08:48 PM

Ok I must have had it backwards. I have learned this stuff but never use it. In fact I took a SAS forecasting course from Dave Dickey. If I remember correctly, I believe he/materials for the course recommended that we use the zero-mean number. I am assuming that the SAS documentation is correct so I'm trying to come up with an answer that fits, so my new one is that the statement that both series have a unit root is by looking at the zero (or single) mean series and seeing that for both Y's, the DF statistics are not significant.

I think I have some notes on the difference between rho and tau as well... If you're interested I'll try to find them when I get back in the office on Monday.