## regression of nonstationary time series

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### regression of nonstationary time series

Hi All

i regressed a nonstationary time series y and got a result as follows

y = 1.006 y(-1) + 0.003 x - 0.002 z + e

y includes a unit root.
Then, is the regression totally useless?
For me, the coefficients seem 'not spurious' at all.
And i am curious whether the AR coefficient sometime exceed one as in the above case.
I politely invite opinion from experts in time series estimation.

Thanks

pamin
pa0326

Posts: 2
Joined: Mon Mar 26, 2012 8:37 am

### Re: regression of nonstationary time series

Send your data to tomdireill@verizon.net and I will take a look. Is your data "explosive"? If it is, then you CAN be this way and make sense. Hamilton talks about MA, but it can also be ok for an AR.

From the Eviews manual:

If has a real root whose absolute value exceeds one or a pair of complex reciprocal rootsoutside the unit circle (that is, with modulus greater than one), it means that the autoregres-sive process is explosive.If has reciprocal roots outside the unit circle, we say that the MA process is noninvertible,which makes interpreting and using the MA results difficult. However, noninvertibility poses no substantive problem, since as Hamilton (1994a, p. 65) notes, there is always an equivalent representation for the MA model where the reciprocal roots lie inside the unit cir-cle. Accordingly, you should re-estimate your model with different starting values until youget a moving average process that satisfies invertibility. Alternatively, you may wish to turnoff MA backcasting (see“Backcasting MA terms” on page102).If the estimated MA process has roots with modulus close to one, it is a sign that you mayhave over-differenced the data. The process will be difficult to estimate and even more diffi-cult to forecast. If possible, you should re-estimate with one less round of differencing.Consider the following example output from ARMA estimation:
tomdireill

Posts: 1
Joined: Fri Jul 09, 2010 11:00 am

### Re: regression of nonstationary time series

The series 'y' is not explosive in a pure AR(1) regression.
It becomes explosive only when the variables 'x' and 'z' are added
to the right-hand side.
pa0326

Posts: 2
Joined: Mon Mar 26, 2012 8:37 am