The RATS Software Forum

ac_1 wrote:Hi Tom,

I am attempting to run a recursive VECM, estimation and one-step ahead OOS forecasts using @JOHMLE.src.

I have two choices, either:
(a) I can "fix" the number of cointegrating vectors from economic theory or from IS estimation, and then run the do loop; or
(b) let the data choose the number of cointegrating vectors based on: if Trace>Trace-95%, traversing down the Rank column, within the loop.

(a) I can do, however how would I do (b) using @JOHMLE.src?

ac_1 wrote: Also, do I have to normalise the cointegrating vectors prior to forecasting?

ac_1 wrote:Many Thanks.

Are the SE's still applicable in FORECAST(STDERRS=...), for graphing PI's in a VECM?

ac_1 wrote:Thanks.

Do you mean short-term forecasting as just one-step ahead?

ac_1 wrote: Questions regarding interpretation and differencing in financial & macro variables:

In single-equation ARMA modelling with stationary I(0) one would expect coefficient betas to be (mostly) between plus/minus 1 implying a non-explosive/non-persistent series. Correct? E.g. Enders AETS Table 2.4 the a1 term is greater than 1 for AR(7), AR(2) and AR(1,2,7), and except for a0 the constant, less than plus/minus 1 in all others.

TomDoan wrote: That's just wrong. Individual coefficients don't tell you anything about whether the model is stationary. The stationary process (1-.9L)^2 y = e, converts to the AR representation (1-1.8L+.81L^2) y = e, or y = 1.8y{1}-.81y{2}+e so the first lag is not just bigger than one but *much* bigger than 1.

ac_1 wrote:

TomDoan wrote: That's just wrong. Individual coefficients don't tell you anything about whether the model is stationary. The stationary process (1-.9L)^2 y = e, converts to the AR representation (1-1.8L+.81L^2) y = e, or y = 1.8y{1}-.81y{2}+e so the first lag is not just bigger than one but *much* bigger than 1.

Yes, understood the algebra. How is (1-.9L)^2 y = e a stationary process?

ac_1 wrote: Do I interpret the weights on the AR lags, in the usual regression way? In an AR(1) 'If y{1} increases by 1 unit, y will be expected, everything else being equal, to increase by phi units'.
Are IRF's (for single equation's) a more appropriate interpretation?

ac_1 wrote: How about the cointegration specifications?

TomDoan wrote: The roots are on the proper side of the unit circle. If you don't know that, you need to review how AR processes work.

equation(noconst,ar=2,coeffs=||+1.8,-0.81||) arma y
*
compute croots=%polycxroots(%eqnlagpoly(arma,y))
disp croots
disp croots(1)
disp croots(2)
*
compute invcroots = 1.0/1.11111
disp 'invcroots:' invcroots
*
compute A1 = 1.0
compute A2 = 1.0
*
cal(irregular)
allocate 100
do t = 1, 100
   set res1 1 100 = A1*(invcroots)^t + A2*(invcroots)^t
end t
*
prin / res1
*
graph 1
# res1

TomDoan wrote: You don't try to "interpret" the individual coefficients. That's why it's considered to be bad form to list the coefficients of a VAR---they provide no useful information. IRF's show the dynamics implied by the process.

compute companion=%modelcompanion(var4model)
eigen(cvalues=cv) companion
disp cv

ac_1 wrote:

TomDoan wrote: The roots are on the proper side of the unit circle. If you don't know that, you need to review how AR processes work.

The discriminant = 0. I get repeated roots = 0.9. The characteristic roots lie inside the unit circle. It's I(0) i.e. stationary. The series is convergent and stable as shown via plotting the time path where the arbitrary constants are set to 1 with t running from 1 to 100.

Code: Select all

equation(noconst,ar=2,coeffs=||+1.8,-0.81||) arma y
*
compute croots=%polycxroots(%eqnlagpoly(arma,y))
disp croots
disp croots(1)
disp croots(2)
*
compute invcroots = 1.0/1.11111
disp 'invcroots:' invcroots
*
compute A1 = 1.0
compute A2 = 1.0
*
cal(irregular)
allocate 100
do t = 1, 100
   set res1 1 100 = A1*(invcroots)^t + A2*(invcroots)^t
end t
*
prin / res1
*
graph 1
# res1

Does the graph tend to zero as that's the mean of this AR(2) without a constant? Is the plot defined as the IRF for an AR process?
If I calculate the inverse roots and plot the graph, I can still make comparisons with information criteria regarding fit of various models.

TomDoan wrote: You don't try to "interpret" the individual coefficients. That's why it's considered to be bad form to list the coefficients of a VAR---they provide no useful information. IRF's show the dynamics implied by the process.

ac_1 wrote:Is it bad form to "interpret" the t-stats for an I(0) AR process?

ac_1 wrote: Also, for e.g. VAR(4)

Code: Select all

compute companion=%modelcompanion(var4model)
eigen(cvalues=cv) companion
disp cv

Has 8 results: the brackets ( , ) to include complex roots; are these the roots or inverse roots?

ac_1 wrote: If I calculate the roots...

ac_1 wrote:Thanks!

For the AR(2) that should say:

ac_1 wrote: If I calculate the roots...

Questions on lag selection:

For variables in levels, let's say from @varlagsselect the number of lags = 2.

Hence, using SYSTEM, for 'like-with-like' comparisons, estimating
(i) a VAR-in-levels: set LAGS = 1 2
(ii) a VAR-in-differences: set LAGS = 1 2
(iii) a VECM: set LAGS = 1 2 3 i.e. 3 lagged levels are equivalent to 2 lagged changes. Therefore the VECM will have 2 lags and ECT('s).

And for @JohMLE for use with the above VECM, LAGS = (2+1)=3.

Correct?

TomDoan wrote: No. If you get @VARLAGSELECT of 2 in levels, then the VAR in differences would be LAGS 1, and @JOHMLE would be LAGS=2.

ac_1 wrote:

TomDoan wrote: No. If you get @VARLAGSELECT of 2 in levels, then the VAR in differences would be LAGS 1, and @JOHMLE would be LAGS=2.

If I get @VARLAGSELECT of 1 in levels, then the VAR in differences would be no lags, and @JOHMLE would be LAGS=1.

Correct?

ac_1 wrote: To confirm:
(a) Unit root tests e.g. ADF: tests if a time series variable is non-stationary and possesses a unit root.
(b) Calculating/Plotting (inverse) characteristic roots of ARIMA models: checks if the sequence generated from the model/specification/process is stable, stationary and invertible.

Correct?