Difference between AR model and distributed lag model

[Anuja Tandon]

Hi,
I was trying to estimate the number of lags of y to be included in an estimateion by looking at its correlogram. I dtermined that it follows a path of AR(2) model. Then if I specify in the equation ar(1) and ar(2) along with the independant variable, then the coefficients of ar(1) and ar(2) are different than if i specify the lags as y(t-1) and y(t-2)? Aren't ar(1) and ar(2) same as y(t-1) and y(t-2)? Also, what is then the difference if I choose ARDL model instead of ARMA model in E-views if it is just an AR(2) model?

[Jesse Wursten]

I think your question refers to the Eviews program. This, unfortunately, is the Stata forum and I don't think many here have any experience with Eviews...

[Anuja Tandon]

Thanks for the answer. In general, my quesry is - In Time Series analysis, what is the differenve between AR(1) model and ARDL model?

[Jesse Wursten]

In an AR(1) model you only lag the dependent variable. In ARDL models you include lags of dependent and independent variables if I'm not mistaken.

[Eric de Souza]

Indeed, the -reg- command and the -arima- command give very different results for an AR(2) model:

use http://www.stata-press.com/data/r14/wpi1.dta
reg L(0/2).wpi
arima wpi, ar(1 2)

Using Stata version 14.2

[Eric de Souza]

wpi is a non-stationary series with a unit root. If I issue the same commands as above using the first difference of wpi, reg and arima give very similar results.

[Sebastian Kripfganz]

The difference between an AR and an ARDL model is that the latter includes additional exogenous variables (and their distributed lags) while the former does not. For the estimation of an ARDL model in Stata, also see: ARDL in Stata.

With regard to the different estimates, regress just delivers OLS estimates conditional on the initial observations. arima uses Kalman filter recursions with random draws from the stationary distribution for the initial conditions. That is why the results differ.

[Anuja Tandon]

Thanks a lot! So basically the only difference betweeb using llagged terms and AR term is in estimation procedure. However, some texts say that if I have such a scenario- y(t)= a*c+ a1*x(t) + u(t) whereby u(t)= b*u(t-1) + v(t) ,so basically there is serial correlation, then ar(1) term should be used.
I have this specification in 2SLS: y(t)= c+ a1*x(t) + a2*z(t) + a3*y(t-1) + error, and the error is serially correlated. The first equation of 2SLS is x(t) = c + b1*y(t-7) + b2*z(t-7) + b3*x(t-1) + b4* x(t-2). Thus, to counter the serial correlation in second equation, should I add ar or ma term?

Thanks!