About TAR Model

[Brc]

Hello Dear Tom,

I have a inflation data set with 265 observations (2003:02 - 2025:02 / monthly)

I have found that lag order is 9 by AIC. That's, the data set Y follows AR(9).

I run the linear regression AR(9) model. And then, I dropped the insignificant lags.
Then, the linear model with significant lags is Y= Y{1} + Y{5} + Y{7} + Y{9}
****
***Linear Model Estmation*******
LINREG(PRINT) Y / RT
# Y{1 5 7 9}
***

Now, I try to determine the transition variable and threshold value.

For that, firstly, I applies HANSEN 1987 Method as follows:

@THRESHTEST(THRESH=Y{4},TRIM=0.15,GRAPH,NREPS=5000) Y
#constant Y{1 5 7 9}
************************************
DISPLAY 'CDSTAT' %CDSTAT 'SIGNIF' %SIGNIF
************************************************

Note that, while I'm applying @THRESHTEST, I ignore the insignificant lags. And I obtained the result that the transition variable is Y{4} (4th lag of Y).

Secondly, I applied CHAN'S method to verify the transition variable and threshold value as follows:

SOURCE C:\RATS-PROCEDURES\TAR.SRC
@TAR(P=9,NREP=3000) Y
*****

However, when I applied CHAN'S method, I obtained the result that the transition variable is Y{2} (2nd lag of Y).


Thirdly, I applied Arranged Autoregression Test as follows:

SOURCE C:\RATS-PROCEDURES\tsaytest.src
DO I=1,9,1
SET THR = Z{i}
@tsaytest(threshold=THR) Z
# constant Z{1 5 7 9}
END DO I
****************************

In this case, I got the result that there is no statistically significant transition variable. Note that while I'm applying @ tsaytest, I ignore the insignificant lags.


*****

My questions:
1) While I'm applying @tsaytest and @THRESHTEST, I ignore the insignificant lags in both test. Is this correct? Or, should I include all 9 lags (in AR(9) model) while doing these tests?

2) While doing these test, should I exclude the highest and lowest 15% of the values form the search? If yes, how?

3) If three tests suggest different transition variables and threshold values, then which test should I prefer?


Thank you for your helps,

Best,

[TomDoan]

The procedure that Terasvirta recommends for a STAR model https://estima.com/webhelp/topics/tarmodelsrpf.html is to keep the full set of lags intact until you have determined how to handle the break. After all, if there is some type of TAR effect (whether the sharp transition or smooth), then the univariate AR is misspecified and pruning lags based upon that may be a mistake.

The calculations in @TAR and @THRESHTEST are fairly similar---@TAR is specifically designed for searching over possible breaks in a self-exciting model. I don't think the Tsay testing method has ever really caught on.

[Brc]

Dear Tom, thank you for your helps.

That's to say, after omitting insignificant lags in linear Model, conducting @THRESHTEST and @tsaytest tests is wrong way.

In brief, these are wrong.

@THRESHTEST(THRESH=Y3,TRIM=0.15,GRAPH,NREPS=5000) Y
# Y{1 5 7 9}
************************************
DISPLAY 'CDSTAT' %CDSTAT 'SIGNIF' %SIGNIF
***************

DO I=1,9,1
SET THR = Y{i}
@tsaytest( threshold=THR) Y
# Y{1 5 7 9}
END DO i
**********

However, these are correct:

@THRESHTEST(THRESH=Y3,TRIM=0.15,GRAPH,NREPS=5000) Y
#constant Y{1 to 9}
************************************
DISPLAY 'CDSTAT' %CDSTAT 'SIGNIF' %SIGNIF

******

DO I=1,9,1
SET THR = Y{i}
@tsaytest( threshold=THR) Y
#constant Y{1 to 9}
END DO I


*******

Have I understood it correctly? Thank you very much.

[TomDoan]

Yes. Don't cut lags out based upon the results of the non-threshold model.