Estimation Technique ADL /ARMAX Model

[relaxdave]

Hi!

I am writing my bachelor thesis pursuing a GDP-Forecast in a simple one equation model. Is it suitable to estimate an ADL,

e.g. GDP = C + AR(1) + SAR(12) + MA(1) + SMA(12) + Consumption(-1) + TREND

model with nonlinear LS?

I couldn t find an answer in the EViews manual and on the web. Do you have any literature with proofs and explanations to find out which estimator is unbiased and consistent in this case?

Btw: I read pretty often OLS would be consistent for large samples - how many observations are regarded as a "large sample"? I guess it depends on the issue, but how can I find out if my 235 observations are sufficient to argue that my estimator just needs to be consistent and not necessarily unbiased?

Thank you,

Dave

[relaxdave]

nobody there who knows under which assumptions NLS is consistent?

I am looking for a set of assumptions (like Gauss Markov without linearity) which can be checked in the postestimation analysis. So far I just found some not understandable mathematical articles about that.

Thank you for help.

[startz]

If errors are iid normal, then nonlinear least squares is asymptotically equivalent to maximum likelihood. So all the consistency and efficiency properties of maximum likelihood apply.

In your particular model, you may want to think about two specific issues.
(1) Some of your variables are almost certainly nonstationary. This changes the underlying econometric theory, although not necessarily in a bad way.
(2) If you're really interested in forecasting, it's not at all clear that finding the "true" coefficients is very important.

[relaxdave]

Thank you for your answer!

1) Through log transformation and a trending variable I controlled for the nonstationarity and it works fine.
2) I thought the estimated coefficients determine the forecast value, don't they? If I had biased estimators the forecast would be biases as well.

If i get the literature right, Maximum Likelihood is the nonlinear estimator with the most desireable properties (NLS only if u_t iid). So why would I use NLS and not always MLE? What are the advantages of NLS vs. MLE?

Citable Literature would be helpful, because I need to justify in my thesis WHY I used NLS.

Thank you in advance!

[startz]

Thank you for your answer!

1) Through log transformation and a trending variable I controlled for the nonstationarity and it works fine.
2) I thought the estimated coefficients determine the forecast value, don't they? If I had biased estimators the forecast would be biases as well.

If i get the literature right, Maximum Likelihood is the nonlinear estimator with the most desireable properties (NLS only if u_t iid). So why would I use NLS and not always MLE? What are the advantages of NLS vs. MLE?

Citable Literature would be helpful, because I need to justify in my thesis WHY I used NLS.

Thank you in advance!

1) Using a trend variable controls for nonstationarity only if the right model is trend stationary, not if it's difference stationary.
2) Not necessarily. If the coefficients are biased because the variables are correlated with the error and if they are going to be correlated in the same way during the forecast period, then the bias in the coefficients picks up likely information about the future errors.

MLE can be applied for more general error structures. NLS is the same as mle--except for a couple of data points--if the errors are iid normal.

Most of this is in any standard econometrics text (past the very introductory level).