Why does EstimatedProcess (via TimeSereisModelFit) give a different result for the same data than LinearModelFit?

Question

This is a question about Mathematica's behavior. I give some background -- but you can skip to the code block below, which illustrates the behavior.

I am using Mathematica ("WL") to work through the time series examples in Stock and Watson's "Introductory Econometrics" and also to replicate the solutions for those examples in Hanck et al "Using R for 'Introductory Econometrics'". It's fun and I'm learning my way around the WL time series modules.

But a puzzle. I import a spreadsheet via SemanticImport[] into a DataSet and then extract the quarterly dates and GDP levels (via Normal[]) into a TimeSeries object.

I transform this TS object into a "GDP Percentage Growth" object by applying 400 Differences[Log[gdplogts]] to the GDP level series.

After imposing a 1962-2012 window on the percentage growth series, I estimate Stock and Watson's AR(1) model (their results: GDPGGsubT = 1.991 + 0.344 GDPGRsubT-1) two different ways:

1: gdpgr6212AR1 = TimeSeriesModelFit[gdpgrpctts6212, {"AR", {1}}]. The intercept, coefficient, and error variance returned are ARProcess[2.023891, {0.3371512}, 9.924687], which are close to the Stock and Watson values, but quite distinguishable from them.

2: I extracted the GDP Growth for 1962:2012 into a list, create level and lag versions of the lists, combine them into a coordinate array with MapThread[], and then submit this array to LinearModelFit[]. Here the Normal[] reduction of the FittedModel returns 1.990784 + 0.3436466 x, which rounds exactly to the Stock and Watson textbook result.

My question is, why do these methods produce different results? There are analogous approaches in R to what I did above (none of which match the Stock & Watson result as well as WL LinearModelFit[]), but all of them ultimately seem to be wrappers for the core R lm() ("linear model") estimator and they all return the same results.

In WL, I can't tell whether I am inadvertently introducing the variability, or whether different estimators are used by LinearModelFit[] and EstimateProcess[] (which seems to be what TimeSeriesModelFit[] is pointing to, so I go right to it in the code snippet below).

The code below replicates my actions with a small snippet of the GDP Percentage Growth value list.

Code

(* 10 obs of base series*)
basetestdata = {2845.453, 2873.169, 2843.718, 2770., 2788.278, 
   2852.741, 2919.47, 2973.782, 3046.096, 3040.235};  
(* 10 obs at Lag 1*)
lagtestdata = {2851.778, 2845.453, 2873.169, 2843.718, 2770., 
   2788.278, 2852.741, 2919.47, 2973.782, 3046.096} ;
(* Calculate percentage growth*)
tdgrowthpct = 400  Log[basetestdata/lagtestdata] (* 10 obs*)

(* Method 1: Submit to Estimateprocess[] *)
tdgrowthpctEProc = 
 EstimatedProcess[tdgrowthpct, 
  ARProcess[1]] (* Lag will reduce to 9 obs *)
(* Output is : ARProcess[1.537332, {0.3994062}, 33.70502] *)

(* Method 2: form pairs and submit to LinearModelFit[] R *)
basetdgrowthpct = Take[tdgrowthpct, {2, 10}] (* Get down to 9 obs *)
lagtdgrowthpct = Take[tdgrowthpct, {1, 9}] (* Get down to 9 obs *)
data2 = MapThread[
  List, {lagtdgrowthpct, basetdgrowthpct}] (* Create nine pairs *)
tdgrowthpctLM1 = 
 LinearModelFit[data2, x, x]  // Normal  (* Submit nine pairs *)
(* Output is 1.745164 + 0.408785 x *) 
```

Answer 1

I'm disappointed that this post received no replies. To close the entry off, I will attempt to answer my own question. I will be more than happy to retract the following if a better answer appears.

As far as I can tell LinearModelFit[ ] and the stack of functions such as TimeSeriesModelFit[ ] that boil down to a call to EstimatedProcess[ ] use different estimation routines which produce different results for the same basic OLS-preferred scenarios. LinearModelFit[ ] consistently matches (at least to two decimal points) the small sample results of other packages; TimeSeriesModelFit[ ] does not. The results are not hugely different -- they typically have the same p-values -- but since the differences are unexplainable, it's hard to see how how TimeSeriesModelFit[ ] could be used in original econometric research involving time series or in projects seeking to replicate the results of time series studies conducted on other platforms. This is a shame, because Mathematica is an excellent platform for math-based original and replication projects, but it in the case of econometric projects, it seems it must be used with great care.

Postscript: I appreciate the respinse from @JimB. Based on these, I retract the above conclusion. I was assuming a parallel in usage between TimeSeriesModelFit' and LinearModelFit` which does not really hold.