5:49 p.m.
Hi all, especially Sven,
I was playing with the package thres_infer, and it appears that the threshold estimates
from functions H_thresh_test() and H_thresh_estim() differ. Is it intented? Should they be
the same? In the particular example from the sample script, which I pasted below, the
values are similar, but I run it with data that give totally different results.
Any thought - suggestions?
Best regards,
Andreas
gretl version 2024d
Current session: 2025-04-08 16:37
# Sample script for thresh_infer
Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3
Listing 5 variables:
0) const 1) LRM 2) LRY 3) IBO 4) IDE
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.088000
(46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: mg
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0705718 0.0272334 2.591 0.0096 ***
IBO -0.469693 0.229408 -2.047 0.0406 **
IDE 0.110332 0.500081 0.2206 0.8254
Observations = 54
Degrees of Freedom = 51
Sum of Squared Errors = 0.0487311
Residual Variance = 0.000955512
R-squared = 0.162774
Heterosked. test p-val = 0.365732
*************************************************************
Threshold Estimation, dependent variable: mg
Threshold Variable: IDE
Threshold Estimate = 0.074 90% CI: [0.074, 0.11]
Sum of Sq. Errors = 0.0435625 Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225
*************************************************************
Regime 1: IDE <= 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.833454 0.386015 -2.159 0.0308 **
IBO -0.774593 0.915857 -0.8458 0.3977
IDE 13.4116 6.06844 2.210 0.0271 **
Observations = 5
Degrees of Freedom = 2
Sum of Squared Errors = 0.00612267
Residual Variance = 0.00306133
R-squared = 0.425631
Regime 2: IDE > 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0727286 0.0303053 2.400 0.0164 **
IBO -0.487763 0.233237 -2.091 0.0365 **
IDE 0.116314 0.505722 0.2300 0.8181
Observations = 49
Degrees of Freedom = 46
Sum of Squared Errors = 0.0374399
Residual Variance = 0.000813911
R-squared = 0.178561
7:25 p.m.
Hi Andreas,
that the estimates are usually different is also noted in the help text.
The approaches have different criteria which they implicitly or
explicitly optimize.
In particular, a deeper problem is non-identification of the threshold
estimate under H0, i.e. if no threshold effect exists. In this
situation, various estimators of the non-existing effect could be all
over the place. Do you find clear rejection of the null of no threshold
in your application?
Of course, assuming that a threshold is there, the estimates refer to
the same object/parameter, so if it's "totally different", it's very
understandable that it feels strange. There would be a bunch of possible
reasons for that: econometrically I'd say for example small sample
and/or model mis-specification of various kinds, or in terms of usage
perhaps different implicit option settings for the two approaches? And
finally, to be honest, it's always possible that there's a software bug
somewhere. Maybe you could cross-check with the R-packaged version of
Hansen's code, e.g. this one: https://github.com/mlkremer/thrreg.
Hope this helps
sven
Am 08.04.2025 um 16:49 schrieb Andreas Zervas:
Hi all, especially Sven,
I was playing with the package thres_infer, and it appears that the
threshold estimates from functions H_thresh_test() and
H_thresh_estim() differ. Is it intented? Should they be the same? In
the particular example from the sample script, which I pasted below,
the values are similar, but I run it with data that give totally
different results.
Any thought - suggestions?
Best regards,
Andreas
gretl version 2024d
Current session: 2025-04-08 16:37
# Sample script for thresh_infer
Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3
Listing 5 variables:
0) const 1) LRM 2) LRY 3) IBO 4) IDE
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
*Threshold Estimate: 0.088000*
(46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: mg
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0705718 0.0272334 2.591 0.0096 ***
IBO -0.469693 0.229408 -2.047 0.0406 **
IDE 0.110332 0.500081 0.2206 0.8254
Observations = 54
Degrees of Freedom = 51
Sum of Squared Errors = 0.0487311
Residual Variance = 0.000955512
R-squared = 0.162774
Heterosked. test p-val = 0.365732
*************************************************************
Threshold Estimation, dependent variable: mg
Threshold Variable: IDE
*Threshold Estimate = 0.074 90% CI: [0.074, 0.11]*
Sum of Sq. Errors = 0.0435625 Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225
*************************************************************
Regime 1: IDE <= 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.833454 0.386015 -2.159 0.0308 **
IBO -0.774593 0.915857 -0.8458 0.3977
IDE 13.4116 6.06844 2.210 0.0271 **
Observations = 5
Degrees of Freedom = 2
Sum of Squared Errors = 0.00612267
Residual Variance = 0.00306133
R-squared = 0.425631
Regime 2: IDE > 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0727286 0.0303053 2.400 0.0164 **
IBO -0.487763 0.233237 -2.091 0.0365 **
IDE 0.116314 0.505722 0.2300 0.8181
Observations = 49
Degrees of Freedom = 46
Sum of Squared Errors = 0.0374399
Residual Variance = 0.000813911
R-squared = 0.178561
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8:02 p.m.
Many thanks,
Most likely a small sample problem (the estimate from the first function leaves 18% of
observations in first regime, while that of the second even less). However, maybe you
should decide what is the preferred approach to estimate the threshold, so that results do
not differ.
Many thanks though for the program and the reply.
Best regards,
Andreas
P.S.
The commands I use are (no other parameter is pre-set):
bundle b_nfc_td_@vn = H_thresh_test(d_EA_nfc_td, l1, test_var, FALSE, 1000, 0.95, 0.15)
b_nfc_td_@vn = H_thresh_estim(d_EA_nfc_td, l1, test_var, FALSE, 0.9, 0.7, 2)
and the output is:
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.160979
(18 % of obs in 1st regime)
LM-test for no threshold: 25.684802
Bootstrap p-value: 0.009000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: d_EA_nfc_td
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.00673135 0.00420391 -1.601 0.1093
d_DFR 0.483153 0.0314844 15.35 3.78e-53 ***
d_DFR_1 0.303526 0.0317247 9.567 1.10e-21 ***
d_DFR_2 0.166300 0.0316151 5.260 1.44e-07 ***
d_DFR_3 -0.0447660 0.0312387 -1.433 0.1518
d_DFR_4 -0.0825148 0.0310742 -2.655 0.0079 ***
Observations = 301
Degrees of Freedom = 295
Sum of Squared Errors = 1.56605
Residual Variance = 0.00530865
R-squared = 0.692068
Heterosked. test p-val = 0.000971344
*************************************************************
Threshold Estimation, dependent variable: d_EA_nfc_td
Threshold Variable: test_var
Threshold Estimate = 0.528682 90% CI: [0.528682, 0.528682]
Sum of Sq. Errors = 1.18205 Residual Var. = 0.00409013
Joint R-squared = 0.768
Heterosked. test p-value: 0.000
*************************************************************
Regime 1: test_var <= 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
--------------------------------------------------------
Constant -0.00301783 0.00374876 -0.8050 0.4208
d_DFR 0.434563 0.0285556 15.22 2.68e-52 ***
d_DFR_1 0.329858 0.0284484 11.59 4.37e-31 ***
d_DFR_2 0.173306 0.0281670 6.153 7.61e-10 ***
d_DFR_3 -0.0265575 0.0281749 -0.9426 0.3459
d_DFR_4 -0.0782675 0.0283734 -2.758 0.0058 ***
Observations = 292
Degrees of Freedom = 286
Sum of Squared Errors = 1.14915
Residual Variance = 0.00401801
R-squared = 0.74057
Regime 2: test_var > 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.138555 0.0277248 -4.998 5.81e-07 ***
d_DFR 1.20773 0.142826 8.456 2.77e-17 ***
d_DFR_1 -0.306680 0.156734 -1.957 0.0504 *
d_DFR_2 0.443741 0.237662 1.867 0.0619 *
d_DFR_3 -0.275100 0.169861 -1.620 0.1053
d_DFR_4 0.284360 0.123145 2.309 0.0209 **
Observations = 9
Degrees of Freedom = 3
Sum of Squared Errors = 0.0328959
Residual Variance = 0.0109653
R-squared = 0.934906
On Tuesday, April 8, 2025 at 04:49:22 PM GMT+2, Andreas Zervas
<anzervas(a)yahoo.com> wrote:
Hi all, especially Sven,
I was playing with the package thres_infer, and it appears that the threshold estimates
from functions H_thresh_test() and H_thresh_estim() differ. Is it intented? Should they be
the same? In the particular example from the sample script, which I pasted below, the
values are similar, but I run it with data that give totally different results.
Any thought - suggestions?
Best regards,
Andreas
gretl version 2024d
Current session: 2025-04-08 16:37
# Sample script for thresh_infer
Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3
Listing 5 variables:
0) const 1) LRM 2) LRY 3) IBO 4) IDE
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.088000
(46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: mg
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0705718 0.0272334 2.591 0.0096 ***
IBO -0.469693 0.229408 -2.047 0.0406 **
IDE 0.110332 0.500081 0.2206 0.8254
Observations = 54
Degrees of Freedom = 51
Sum of Squared Errors = 0.0487311
Residual Variance = 0.000955512
R-squared = 0.162774
Heterosked. test p-val = 0.365732
*************************************************************
Threshold Estimation, dependent variable: mg
Threshold Variable: IDE
Threshold Estimate = 0.074 90% CI: [0.074, 0.11]
Sum of Sq. Errors = 0.0435625 Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225
*************************************************************
Regime 1: IDE <= 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.833454 0.386015 -2.159 0.0308 **
IBO -0.774593 0.915857 -0.8458 0.3977
IDE 13.4116 6.06844 2.210 0.0271 **
Observations = 5
Degrees of Freedom = 2
Sum of Squared Errors = 0.00612267
Residual Variance = 0.00306133
R-squared = 0.425631
Regime 2: IDE > 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0727286 0.0303053 2.400 0.0164 **
IBO -0.487763 0.233237 -2.091 0.0365 **
IDE 0.116314 0.505722 0.2300 0.8181
Observations = 49
Degrees of Freedom = 46
Sum of Squared Errors = 0.0374399
Residual Variance = 0.000813911
R-squared = 0.178561
9:24 p.m.
Thanks for sharing your output - some comments...
Am 08.04.2025 um 19:02 schrieb Andreas Zervas:
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.160979
(18 % of obs in 1st regime)
LM-test for no threshold: 25.684802
Bootstrap p-value: 0.009000
OK, so nominally the absence of a threshold effect is rejected.
However,
Heterosked. test p-val = 0.000971344
... your assumption of homoskedasticity
above does not seem to be
warranted, so the nominal threshold test result may be dubious. (And so
could be the implied threshold estimate from this approach.)
*************************************************************
Threshold Estimation, dependent variable: d_EA_nfc_td
Threshold Variable: test_var
Threshold Estimate = 0.528682 90% CI: [0.528682, 0.528682]
This confidence interval with length zero seems weird. I guess with a
finite set of potential threshold values it could happen in theory, but
still; also your variable seems more or less continuous, right? I will
try to take a look what's happening in the code, but if you could share
your dataset (off-list if you like) that might be helpful.
Regime 2: test_var > 0.528682
...
Observations = 9
Degrees of Freedom = 3
Hm, obviously very few obs left in that regime, 9/301 = 3%. Not sure why
Hansen didn't implement or require any trimming for the estimation
routine (as opposed to the testing routine). So basically the
H_thresh_test function is prevented from entering that parameter region
by the trimming constraint. This of course is another (not previously
mentioned) reason why the estimates differ.
cheers
sven
3:56 p.m.
Dear Sven,
Thank you for the suggestions. I attach the data and a minimal program to replicate the
results. Any feedback or change in the code is welcome.
Best regards,
Andreas
On Tuesday, April 8, 2025 at 07:02:22 PM GMT+2, Andreas Zervas
<anzervas(a)yahoo.com> wrote:
Many thanks,
Most likely a small sample problem (the estimate from the first function leaves 18% of
observations in first regime, while that of the second even less). However, maybe you
should decide what is the preferred approach to estimate the threshold, so that results do
not differ.
Many thanks though for the program and the reply.
Best regards,
Andreas
P.S.
The commands I use are (no other parameter is pre-set):
bundle b_nfc_td_@vn = H_thresh_test(d_EA_nfc_td, l1, test_var, FALSE, 1000, 0.95, 0.15)
b_nfc_td_@vn = H_thresh_estim(d_EA_nfc_td, l1, test_var, FALSE, 0.9, 0.7, 2)
and the output is:
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.160979
(18 % of obs in 1st regime)
LM-test for no threshold: 25.684802
Bootstrap p-value: 0.009000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: d_EA_nfc_td
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.00673135 0.00420391 -1.601 0.1093
d_DFR 0.483153 0.0314844 15.35 3.78e-53 ***
d_DFR_1 0.303526 0.0317247 9.567 1.10e-21 ***
d_DFR_2 0.166300 0.0316151 5.260 1.44e-07 ***
d_DFR_3 -0.0447660 0.0312387 -1.433 0.1518
d_DFR_4 -0.0825148 0.0310742 -2.655 0.0079 ***
Observations = 301
Degrees of Freedom = 295
Sum of Squared Errors = 1.56605
Residual Variance = 0.00530865
R-squared = 0.692068
Heterosked. test p-val = 0.000971344
*************************************************************
Threshold Estimation, dependent variable: d_EA_nfc_td
Threshold Variable: test_var
Threshold Estimate = 0.528682 90% CI: [0.528682, 0.528682]
Sum of Sq. Errors = 1.18205 Residual Var. = 0.00409013
Joint R-squared = 0.768
Heterosked. test p-value: 0.000
*************************************************************
Regime 1: test_var <= 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
--------------------------------------------------------
Constant -0.00301783 0.00374876 -0.8050 0.4208
d_DFR 0.434563 0.0285556 15.22 2.68e-52 ***
d_DFR_1 0.329858 0.0284484 11.59 4.37e-31 ***
d_DFR_2 0.173306 0.0281670 6.153 7.61e-10 ***
d_DFR_3 -0.0265575 0.0281749 -0.9426 0.3459
d_DFR_4 -0.0782675 0.0283734 -2.758 0.0058 ***
Observations = 292
Degrees of Freedom = 286
Sum of Squared Errors = 1.14915
Residual Variance = 0.00401801
R-squared = 0.74057
Regime 2: test_var > 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.138555 0.0277248 -4.998 5.81e-07 ***
d_DFR 1.20773 0.142826 8.456 2.77e-17 ***
d_DFR_1 -0.306680 0.156734 -1.957 0.0504 *
d_DFR_2 0.443741 0.237662 1.867 0.0619 *
d_DFR_3 -0.275100 0.169861 -1.620 0.1053
d_DFR_4 0.284360 0.123145 2.309 0.0209 **
Observations = 9
Degrees of Freedom = 3
Sum of Squared Errors = 0.0328959
Residual Variance = 0.0109653
R-squared = 0.934906
On Tuesday, April 8, 2025 at 04:49:22 PM GMT+2, Andreas Zervas
<anzervas(a)yahoo.com> wrote:
Hi all, especially Sven,
I was playing with the package thres_infer, and it appears that the threshold estimates
from functions H_thresh_test() and H_thresh_estim() differ. Is it intented? Should they be
the same? In the particular example from the sample script, which I pasted below, the
values are similar, but I run it with data that give totally different results.
Any thought - suggestions?
Best regards,
Andreas
gretl version 2024d
Current session: 2025-04-08 16:37
# Sample script for thresh_infer
Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3
Listing 5 variables:
0) const 1) LRM 2) LRY 3) IBO 4) IDE
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.088000
(46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: mg
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0705718 0.0272334 2.591 0.0096 ***
IBO -0.469693 0.229408 -2.047 0.0406 **
IDE 0.110332 0.500081 0.2206 0.8254
Observations = 54
Degrees of Freedom = 51
Sum of Squared Errors = 0.0487311
Residual Variance = 0.000955512
R-squared = 0.162774
Heterosked. test p-val = 0.365732
*************************************************************
Threshold Estimation, dependent variable: mg
Threshold Variable: IDE
Threshold Estimate = 0.074 90% CI: [0.074, 0.11]
Sum of Sq. Errors = 0.0435625 Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225
*************************************************************
Regime 1: IDE <= 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.833454 0.386015 -2.159 0.0308 **
IBO -0.774593 0.915857 -0.8458 0.3977
IDE 13.4116 6.06844 2.210 0.0271 **
Observations = 5
Degrees of Freedom = 2
Sum of Squared Errors = 0.00612267
Residual Variance = 0.00306133
R-squared = 0.425631
Regime 2: IDE > 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0727286 0.0303053 2.400 0.0164 **
IBO -0.487763 0.233237 -2.091 0.0365 **
IDE 0.116314 0.505722 0.2300 0.8181
Observations = 49
Degrees of Freedom = 46
Sum of Squared Errors = 0.0374399
Residual Variance = 0.000813911
R-squared = 0.178561
7:31 p.m.
Hi Andreas,
thanks a lot. I think the crucial point really is to note that the
threshold estimation is always conditional on a threshold being present
in the first place. Maybe I can extend the printed output a little in a
future version to make this clearer.
So when I run your application with the heterosked. switch set to
on/TRUE, then everything makes sense: The test result says "LM-test for
no threshold: 7.864104 / Bootstrap p-value: 0.778000", so no threshold
is found. Hence the following threshold estimation should probably be
ignored.
Numerically, the new (90%) CI under heteroskedasticity is then
[0.505766, 0.597225]. Looking at the sorted version of your threshold
variable "test_var", the relevant portion is:
2000:05 0.505766
2004:06 0.515507
2015:01 0.528682
2011:08 0.597225
So the algorithm says that at the 90% level the threshold would be among
one of those four realizations in the sample. Previously, (under the
false assumption of homoskedasticity) the CI was completely focused on
the one realization 0.528682. I readily admit that it's a little
counter-intuitive that with a non-existing / non-identified threshold
the notional CI is very tight instead of very loose, but then we need to
remember that the estimate puts the threshold at a pretty extreme value
into the trimming range of the test. (As before, with only 3% of the
observations in the 2nd regime here.)
@Note to self: The plot "F Test For Threshold" has a strange scaling of
the x-axis. It seems to fit the lhs variable d_EA_nfc_td better than the
threshold (and x-axis label) variable test_var. (This problem does not
appear with the sample script.)
Bottom line: Fortunately I cannot see any substantial problem with the
package here, it's almost all about the funny data that you have which
imply a lot of clear heteroskedasticity.
cheers
sven
Am 09.04.2025 um 14:56 schrieb Andreas Zervas:
Dear Sven,
Thank you for the suggestions. I attach the data and a minimal program
to replicate the results. Any feedback or change in the code is welcome.
Best regards,
Andreas
On Tuesday, April 8, 2025 at 07:02:22 PM GMT+2, Andreas Zervas
<anzervas(a)yahoo.com> wrote:
Many thanks,
Most likely a small sample problem (the estimate from the first
function leaves 18% of observations in first regime, while that of the
second even less). However, maybe you should decide what is the
preferred approach to estimate the threshold, so that results do not
differ.
Many thanks though for the program and the reply.
Best regards,
Andreas
P.S.
The commands I use are (no other parameter is pre-set):
bundle b_nfc_td_@vn = H_thresh_test(d_EA_nfc_td, l1, test_var, FALSE,
1000, 0.95, 0.15)
b_nfc_td_@vn = H_thresh_estim(d_EA_nfc_td, l1, test_var, FALSE, 0.9,
0.7, 2)
and the output is:
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
Threshold Estimate: 0.160979
(18 % of obs in 1st regime)
LM-test for no threshold: 25.684802
Bootstrap p-value: 0.009000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: d_EA_nfc_td
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.00673135 0.00420391 -1.601 0.1093
d_DFR 0.483153 0.0314844 15.35 3.78e-53 ***
d_DFR_1 0.303526 0.0317247 9.567 1.10e-21 ***
d_DFR_2 0.166300 0.0316151 5.260 1.44e-07 ***
d_DFR_3 -0.0447660 0.0312387 -1.433 0.1518
d_DFR_4 -0.0825148 0.0310742 -2.655 0.0079 ***
Observations = 301
Degrees of Freedom = 295
Sum of Squared Errors = 1.56605
Residual Variance = 0.00530865
R-squared = 0.692068
Heterosked. test p-val = 0.000971344
*************************************************************
Threshold Estimation, dependent variable: d_EA_nfc_td
Threshold Variable: test_var
Threshold Estimate = 0.528682 90% CI: [0.528682, 0.528682]
Sum of Sq. Errors = 1.18205 Residual Var. = 0.00409013
Joint R-squared = 0.768
Heterosked. test p-value: 0.000
*************************************************************
Regime 1: test_var <= 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
--------------------------------------------------------
Constant -0.00301783 0.00374876 -0.8050 0.4208
d_DFR 0.434563 0.0285556 15.22 2.68e-52 ***
d_DFR_1 0.329858 0.0284484 11.59 4.37e-31 ***
d_DFR_2 0.173306 0.0281670 6.153 7.61e-10 ***
d_DFR_3 -0.0265575 0.0281749 -0.9426 0.3459
d_DFR_4 -0.0782675 0.0283734 -2.758 0.0058 ***
Observations = 292
Degrees of Freedom = 286
Sum of Squared Errors = 1.14915
Residual Variance = 0.00401801
R-squared = 0.74057
Regime 2: test_var > 0.528682
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.138555 0.0277248 -4.998 5.81e-07 ***
d_DFR 1.20773 0.142826 8.456 2.77e-17 ***
d_DFR_1 -0.306680 0.156734 -1.957 0.0504 *
d_DFR_2 0.443741 0.237662 1.867 0.0619 *
d_DFR_3 -0.275100 0.169861 -1.620 0.1053
d_DFR_4 0.284360 0.123145 2.309 0.0209 **
Observations = 9
Degrees of Freedom = 3
Sum of Squared Errors = 0.0328959
Residual Variance = 0.0109653
R-squared = 0.934906
On Tuesday, April 8, 2025 at 04:49:22 PM GMT+2, Andreas Zervas
<anzervas(a)yahoo.com> wrote:
Hi all, especially Sven,
I was playing with the package thres_infer, and it appears that the
threshold estimates from functions H_thresh_test() and
H_thresh_estim() differ. Is it intented? Should they be the same? In
the particular example from the sample script, which I pasted below,
the values are similar, but I run it with data that give totally
different results.
Any thought - suggestions?
Best regards,
Andreas
gretl version 2024d
Current session: 2025-04-08 16:37
# Sample script for thresh_infer
Read datafile C:\Program Files\gretl\data\misc\denmark.gdt
periodicity: 4, maxobs: 55
observations range: 1974:1 to 1987:3
Listing 5 variables:
0) const 1) LRM 2) LRY 3) IBO 4) IDE
Test of Null of No Threshold Against Alternative of Threshold
Under Maintained Assumption of Homoskedastic Errors
Number of Bootstrap Replications: 1000
Trimming percentage: 0.150000
*Threshold Estimate: 0.088000*
(46 % of obs in 1st regime)
LM-test for no threshold: 4.154898
Bootstrap p-value: 0.923000
*******************************************
Threshold regression based on Hansen (2000)
User choice: assume homoskedasticity
*******************************************
Global OLS Estimation, Without Threshold
Dependent Variable: mg
OLS Standard Errors Reported
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0705718 0.0272334 2.591 0.0096 ***
IBO -0.469693 0.229408 -2.047 0.0406 **
IDE 0.110332 0.500081 0.2206 0.8254
Observations = 54
Degrees of Freedom = 51
Sum of Squared Errors = 0.0487311
Residual Variance = 0.000955512
R-squared = 0.162774
Heterosked. test p-val = 0.365732
*************************************************************
Threshold Estimation, dependent variable: mg
Threshold Variable: IDE
*Threshold Estimate = 0.074 90% CI: [0.074, 0.11]*
Sum of Sq. Errors = 0.0435625 Residual Var. = 0.000907553
Joint R-squared = 0.252
Heterosked. test p-value: 0.225
*************************************************************
Regime 1: IDE <= 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant -0.833454 0.386015 -2.159 0.0308 **
IBO -0.774593 0.915857 -0.8458 0.3977
IDE 13.4116 6.06844 2.210 0.0271 **
Observations = 5
Degrees of Freedom = 2
Sum of Squared Errors = 0.00612267
Residual Variance = 0.00306133
R-squared = 0.425631
Regime 2: IDE > 0.074000
(standard errors do not take into account threshold uncertainty)
coefficient std. error z p-value
-------------------------------------------------------
Constant 0.0727286 0.0303053 2.400 0.0164 **
IBO -0.487763 0.233237 -2.091 0.0365 **
IDE 0.116314 0.505722 0.2300 0.8181
Observations = 49
Degrees of Freedom = 46
Sum of Squared Errors = 0.0374399
Residual Variance = 0.000813911
R-squared = 0.178561
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5 comments
2 participants
participants (2)
-
Andreas Zervas -
Sven Schreiber