This Stata Threshold Vector Autoregression (TVAR) program package estimates the TVAR(2) model and implement a grid search for the optimal threshold parameter.
For users' convenience, files are zipped as TVAR.zip.
The directory /prog/ contains programs :
| File Name | Description | |
|---|---|---|
| 1. | prog/installation.do | Initialisation of the environment for the program package |
| 2. | prog/estimation/TVAR_2r.ado | The main program to estimate a 2-regime TVAR |
| 3. | prog/help/TVAR_2r.sthlp | The help file for TVAR_2r |
| 4. | prog/estimation/TVAR_est.ado | A helper program for estimating a TVAR model |
| 5. | prog/estimation/var_mle.ado | A helper program to estimate the TVAR using the maximum likelihood |
| 6. | prog/estimation/var_ols.ado | A helper program to estimate the TVAR using the ordinary least square |
| 7. | prog/grid_search/grid_search.ado | The main (wrapper) program to implement grid searches for a TVAR model |
| 8. | prog/grid_search/grid_search_op.ado | A helper program for a TVAR model's grid searches |
| 9. | prog/help/TVAR_2r_grid_search.sthlp | The help file for TVAR_2r_grid_search |
| 10. | prog/monte/bootstrap.ado | A program to implement bootstrapping re-sampling process |
| 11. | prog/monte/normal_simulation.ado | A program to implement a Monte Carlo Simulation for TVAR using random variables of uniform[0,1] and Normal(0,1) |
| 12. | prog/monte/test_normal_simulation.ado | A wrapper program for implementing the above Monte Carlo simulation |
Please install associated files before running examples below.
. webuse set http://www.stata.com/users/dschenck/
. webuse usmacro.dta
Assume that observations with an odd index belongs to Regime 1. Other observations belong to Regime 0.
. gen ind = 0
. replace ind = 1 if mod(_n,2) == 1
Fit TVAR(2) by OLS with constant, 1 lag (the default), 0 delay (the default) and dln_m1 being the threshold variable from the fifth observation to the 200th observation.
. TVAR_2r unrate inflation in 5/200, indicator(ind) nlag(1) d(0) constant(1) ols(1)
. TVAR_2r unrate inflation in 5/200, indicator(ind) nlag(1) d(0) constant(1) ols(1)
(8 observations deleted)
Threshold Vector Autoregression with 2 Regimes ( TVAR(2) ): Estimation
Dependent Variables : unrate inflation
Indicator Variable : ind
Delay Parameter (d) : 0
Number of Lags (nlag) : 1/1
Constant? : Yes
Estimation Method : Ordinary Least Square (OLS) Estimation
Estimation Results:
---------------------------------------------------------------------------
Regime Parms R^2 RMSE Sample Size Success?
---------------------------------------------------------------------------
0 6 0.8927 0.7851 98 Yes
1 6 0.9019 0.7513 98 Yes
No Regime 6 0.9641 0.4532 196 Yes
---------------------------------------------------------------------------
------------------------------------------------------------------
Regime | Coefficients
---------------+--------------------------------------------------
Regime 0 |
|
unrate: |
_cons | 0.5244
L1.unrate | 0.8364
L1.inflation | 0.1121
|
inflation: |
_cons | 1.7294
L1.unrate | -0.2636
L1.inflation | 0.9604
|
---------------+--------------------------------------------------
Regime 1 |
|
unrate: |
_cons | 0.5231
L1.unrate | 0.8369
L1.inflation | 0.1119
|
inflation: |
_cons | 1.7266
L1.unrate | -0.2666
L1.inflation | 0.9648
|
---------------+--------------------------------------------------
No Regime |
|
unrate: |
_cons | 0.1607
L1.unrate | 0.9369
L1.inflation | 0.0542
|
inflation: |
_cons | 0.9716
L1.unrate | -0.1600
L1.inflation | 0.9955
|
------------------------------------------------------------------
.
. webuse m1gdp
. tsset t
. drop if ln_m1==.
. gen dln_m1 = d.ln_m1
. gen dln_gdp = d.ln_gdp
Perform a grid search for the optimal threshold value for TVAR consisting of dln_gdp and dln_m1 (with constant). dln_m1 is the threshold variable. Trim is set to 15%. Both lag order and delay parameter are set to 1. The estimation is conducted via OLS. We also impose restriction on sample period.
. TVAR_2r_grid_search dln_gdp dln_m1 if t>=tq(1980q1), threshold(dln_m1) ptrim(0.15) d(1) nlag(1) constant(1) ols(1)
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Hansen, B. (1999). Testing for linearity. Journal of Economic Surveys, 13(5):551–576.
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Hansen, B. E. (1996a). Estimation of TAR Models. Boston College Working Papers in Economics 325., Boston College Department of Economics.
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Hansen, B. E. (1996b). Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica, 64(2):413–430.
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Lo, M. C. and Zivot, E. (2001). Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price. Macroeconomic Dynamics, 5(04):533–576.
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Tsay, R. S. (1998). Testing and modeling multivariate threshold models. Journal of the American Statistical Association, 93(443):1188–1202.