[R] R vs EViews - serial correlation
Patrick Brandt
brandt at unt.edu
Thu Sep 23 20:24:12 CEST 2004
The issue here is that you have confused an AR(1) process for the
variable of interest with an AR(1) process for its residuals. The
former is a true AR(1) process, while the latter is really an MA(1)
process, in terms of Box-Jenkins style ARIMA models.
Interpreting your original post:
> I met with some problems when dealing with a time series with serial correlation.
>
> FIRST, I generate a series with correlated errors
>
> set.seed(1)
> x=1:50
> y=x+arima.sim(n = 50, list(ar = c(0.47)))
This generates an ARIMA(1,0,0) dataset of 50 observations. So the d.v.
has an AR(1) process.
>
> SECOND, I estimate three constants (a, b and rho) in the model Y=a+b*X+u, where u=rho*u(-1)+eps
>
> library(nlme)
> gls(y~x,correlation = corAR1(0.5)) # Is it the right procedure?
>
> Coefficients:
> (Intercept) x
> 0.1410465 1.0023341
>
> Correlation Structure: AR(1)
> Formula: ~1
> Parameter estimate(s):
> Phi
> 0.440594
> Degrees of freedom: 50 total; 48 residual
> Residual standard error: 0.9835158
>
This estimates an AR(1) error process model -- or an ARIMA(0,0,1). By
the Wold decomposition, the AR(1) dgp we should expect the MA(q) process
to have a longer order than 1.
> THIRD, I do the same procedure with EViews as LS Y C X AR(1) and get
> Y = 0.1375 + 1.0024*X + [AR(1)=0.3915]
>
This fits an AR(1) error process (ARIMA(0,0,1)) if I recall my Eviews
syntax.
> My problem is actually connected with the fitting procedure. As far as I understand
>
> gls(y~x,correlation = corAR1(0.5))$fit
>
> is obtained through the linear equation 0.1410+1.0023*X while in EViews through the nonlinear equation
>
> Y=rho*Y(-1) + (1-rho)*a+(X-rho*X(-1))*b
>
> where either dynamic or static fitting procedures are applied.
>
> X Y YF_D YF_S gls.fit
> 1 1 1.1592 NA NA 1.1434
> 2 2 3.5866 2.1499 2.1499 2.1457
> 3 3 4.1355 3.1478 3.7103 3.1480
> 4 4 3.9125 4.1484 4.5352 4.1504
> 5 5 2.7442 5.1502 5.0578 5.1527
> 6 6 6.0647 6.1523 5.2103 6.1551
> 7 7 6.9855 7.1547 7.1203 7.1574
> .....................................
> 47 47 49.4299 47.2521 47.5288 47.2507
> 48 48 48.7748 48.2545 49.1072 48.2531
> 49 49 48.3200 49.2570 49.4607 49.2554
> 50 50 50.2501 50.2594 49.8926 50.2578
Again, both of the models you fit are NOT the DGP you simulated.
>
> All gls.fit values are on a line, YF_D (D for dynamic) soon begin
> to follow a line and YF_S try to mimic Y.
>
Correct since you are fitting a model of correlated INNOVATIONS, rather
than a model of correlated Y's
> My question is: do R and EViews estimate the same model? If yes, why
> the estimates are different and which of the two (three?) procedures
> is "correct"?
>
If you want to fit the DGP you proposed above, you should use
arima(y, order=c(1,0,0), xreg=x)
Hope that helps.
--
Patrick T. Brandt
Assistant Professor
Department of Political Science
University of North Texas
brandt at unt.edu
http://www.psci.unt.edu/~brandt
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