Hi Tom,

A few questions:

1)

A simple example using Engle and Granger:

Code: Select all

```
* LHS first-differences = c + RHS in first-differences + ECT's
*===============================
linreg(define=eq1) x start+1 begin resids1
# constant y
system(model=ectmodel1) 1 to 2
variables dx dy
lags 1 to 2
det constant resids1{1}
end(system)
estimate(noftests) start+1 begin
compute aic = %nobs*%logdet + 2*(((2*2)+1+1)*2)
compute sbc = %nobs*%logdet + (((2*2)+1+1)*2)*log(%nobs)
dis 'aic = ' aic 'sbc = ' sbc
```

Equivalently, as:

Code: Select all

```
* LHS in levels = c + RHS in first-differences + ECT's
*===============================
linreg(define=eq1) x start+1 begin resids1
# constant y
system(model=ectmodel2)
variables x y
lags 1 2 3; * 3 lagged levels are equivalent to 2 lagged changes
det constant
ect eq1
end(system)
estimate(print,resids=resids,noftests) start+2 begin
compute aic = %nobs*%logdet + 2*(((2*2)+1+1)*2)
compute sbc = %nobs*%logdet + (((2*2)+1+1)*2)*log(%nobs)
dis 'aic = ' aic 'sbc = ' sbc
```

ectmodel1 and ectmodel2 have the

same aic & sbc, and the

same coeffs for all variables, but the

ECT's have different signs in each model, and importantly the

LHS's are different.

So how do I interpret the specifications? Is it

LHS is the first-difference = c + RHS in first-differences + ECT's

Or

LHS is the level = c + RHS in first-differences + ECT's ?

2)

I am using Johansen in all VECM analysis, as here:

https://www.estima.com/ratshelp/index.h ... dure.html , and the LHS of the Error Correction Model is in levels.

Enders(2014) AETS, says the Johansen procedure is nothing more than a multivariate generalization of the Dickey–Fuller test. But isn't calculating the ECT's similar to calculating principal components (which happen to be stationary)?

3)

Is it fair to say

'rival' or comparison models for a VAR(p) in levels are:

(i) a VAR(p-1) in first-differences

(ii) a VECM(p-1, Max (p-1) cointegrating vector's), as a VECM is just a VAR in first-differences with a maximum of (p-1) cointegrating vector's.

Or would a more fair comparison be: A VAR(4) in levels, versus a VAR(4) in first-differences, versus a VECM(4, Max (4-1) cointegrating vector's)?

4)

In ECT.RPF, User's Guide, Section 7.8, the unit root test's say all 3 series: ftbs3, ftb12, fcm7 are I(1). Graphically all 3 series show no strong trend. So the series are non-stationary as per ADF (even if I include a TREND term in @dfunit(lags=6,trend)) despite visually having no strong trend. How can that be?

Also with,

@johmle(lags=6,det=rc,cv=cvector)

what affect does DET=RC (restricted constant) have, compared to DET=CONSTANT?

5)

Generating multi-step ahead forecasts from a VAR(p) in first-differences I get

wider fans than comparing fans from a VAR(p) in levels. Is that to be expected?

I am aggregating the forecast SE's as per here:

https://estima.com/forum/viewtopic.php ... 4&start=15, for a VAR(p) in first-differences, but there

was not a solution to why these

* forecast SE's of the DIFFERENCE series

prin / s(1) s(2) s(3) s(4)

prin / COREERRORS(1) COREERRORS(2) COREERRORS(3) COREERRORS(4)

were not the same, and they should be?

To aggregate back to levels, I am using

* forecast SE's of the ORIGINAL series in LEVELS

prin / COREERRORS(5) COREERRORS(6) COREERRORS(7) COREERRORS(8)

Also, if I am modelling term structure of interest rates for a single country, should I

log-transform all series, as that will restrict the fans in all models: VAR in levels, VAR in first-difference, and VECM; to being greater than zero; as one could say negative interest rates are unlikely, unless it's Japan?

Further, how much emphasis should be placed on the interpretation in the

magnitude & sign of the coefficients in all models, especially the ECT (speed of adjustment) parameters?

thanks,

Amarjit