TSMT 2.1: Estimation of Threshold Autoregressive Models

Estimating the TAR Model

This example follows the empirical example found in Hansen (1996) and estimates a threshold model for quarterly GNP growth rates. The data file gnp.dat contains seasonable adjusted GNP for 1947 to 1990 and is transformed to annualized quarterly growth rates:

//Load TSMT library
library tsmt;

//Real GNP data
//Seasonally adjusted and transformed in annualized quarterly growth rates
//1947-1990
//Load 'real_gnp' variable and perform 'ln' transformation
ln_gnp = loadd(__FILE_DIR $+ "gnp_4790.csv", "ln(real_gnp)");

y = (ln_gnp[2:rows(ln_gnp)] - ln_gnp[1:rows(ln_gnp)-1])*400;

Next all parameter values for the TAR estimation must be set

//Declare the structure
struct TARControl TAR0;

//Initialize the structure
TAR0 = TARControlCreate();

//Maximum number of lags considered
TAR0.p = 5;

//Lags to omit from the test
TAR0.omit = { 3, 4 };

//Trimming from top (r1) and bottom (r2) of data
TAR0.lowerQuantile = .15;
TAR0.upperQuantile = .85;

//Number of replications for Monte Carlo
TAR0.rep = 5000;

//Output and graph reporting
TAR0.printOutput = 1;
TAR0.graph = 1;

//Data start date and frequency
TAR0.dstart = 1947;
TAR0.freq = 4;

Finally, call the GAUSS procedure TARTest.

//Declare output structure
struct TAROut TARoutput;

//Estimate model
TARoutput = TARTest(y,TAR0);

This produces three graphs: and prints the following output to the command/program window:

OLS Estimation of Null Linear Model

Variable            Estimate             S.E.
C                   1.99225488           0.59341810
Y(t-1)              0.31753696           0.08929921
Y(t-2)              0.13197878           0.08801236
Y(t-5)             -0.08696297           0.06763670

Residual Variance                   15.960496

Searching over Threshold Variable:              1
Searching over Threshold Variable:              2
Searching over Threshold Variable:              3
Global Estimates
Threshold Variable Lag               2.0000000
Threshold Estimate                 0.012572093
Error Variance                       14.548361

Regime 1: Y(t-2) < 0.012572

Variable            Estimate             S.E.
C                  -3.21255539           2.12039565
Y(t-1)              0.51278104           0.24699822
Y(t-2)             -0.92692272           0.30831951
Y(t-5)              0.38445656           0.24603002

Regime 1 Error Variance             23.533054

Regime 2: Y(t-2) > 0.012572

Variable            Estimate             S.E.
C                   2.14186153           0.77389336
Y(t-1)              0.30085440           0.10132777
Y(t-2)              0.18484356           0.10131018
Y(t-5)             -0.15813482           0.07335517

Regime 2 Error Variance             12.143010

Test Statistics and Estimated Asymptotic P-Values

Robust LM Statistics
SupLM              14.06847762          0.16940000
ExpLM               3.96481133          0.16620000
AveLM               4.68986250          0.27380000

Standard LM Statistics
SupLMs             18.24477743          0.94380000
ExpLMs              4.77627149          0.94320000
AveLMs              4.57209118          0.87960000